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## Risk of using Random Generator instead SecureRandom generator

What are the real-world implications of using java Random generator? What are the practical types of attacks possible? How easy is it to exploit this?

## How to generate random waves for a bullet hell game that feel balanced and natural

My game consists of ‘waves’ of objects called ‘spawners’, which once every certain amount of time (their firetime), move to a new place on the screen and spawn an enemy. Each wave has 4 important properties:
1: the amount of spawners the wave has
2: the interval of time between creating new spawners
3: the total length of the wave
4: the types of spawners that can appear in a wave (represented as a std::vector<std::pair<std::string, int>> where the string is the spawner name, and the integer is its spawn weight.

The game works by picking a random spawner from the possible spawner types (with a weighted rng) every new spawner interval. Currently waves are set and are loaded from a file at runtime.

My problem is that I cannot find a good way to randomly generate waves that feel balanced and natural. Currently, I am trying to generate waves based on a difficulty value, mostly using weighted random number generation. However, this does not produce balanced waves that correspond well to the target difficulty. Even after trying several different techniques, I am unable to get a system that generates waves that fell balanced and natural (like the ones hand made).

Is there any way to generate waves that feel natural, based off of the difficulty value? How should I approach this problem?

Also if its of any help, each spawner also defines its own difficulty value.

## Comparison of feature importance values in logistic regression and random forest in scikitlearn [closed]

I am trying to rank the features for binary classification, based on their importance using an ensemble method by combining the feature importances estimated by random forest and logistic regression. I know that logisticregression coefficients and random forest feture_importances are different values and Im looking for a method to make them comparable. Here is what I have in mind:

X=features y=lablels rf=RandomForestClassifier() rf.fit(X,y) RFfitIMP=rf.feature_importances_/rf.feature_importances_.sum() #normalizing feature importances to sum up to 1 lr=LogisticRegression() lr.fit(X,y) lrfitIMP=np.absolute(lr.coef_)/np.absolute(lr.coef_).sum() #Taking absolute values and normalizing coefficient values to sum up to 1 ensembleFitIMP = np.mean([featIMPs for featIMPs in [RFfitIMP,lrfitIMP]], axis=0)

What I think the code does is to take the relative importance from both models, normalize them and returns the importance of features averaged over two models. I was wondering whether it is a correct approach for this purpose or not?

## Diameter of a random graph

I’m considering the standard Erdös/Renyi $$G(n,p)$$ model where we have $$n$$ nodes and each possible edge is sampled independently with probability $$p = \frac{1}{n^\epsilon}$$.

It is relatively straightforward to show that, starting from any node $$u$$, the expected number of hops to reach every other node is $$1/\epsilon$$. However, this does not say much about the probability of having a diameter of $$1/\epsilon$$. (I could apply Markov’s inequality, but that gives a rather weak bound.)

Thus I’m looking for a reference to a concentration result that states that the diameter of such a random graph is $$O(1/\epsilon)$$ with probability at least $$1 – o(1)$$.

## Establish a symmetric key: KDF based on shared secret and random salt or key wrapping?

I am designing a basic KMS based on a simple HSM, I only have access to: AES256, SHA256, PBKDF2, HMAC (and combinations like AES256-HMAC-SHA256). The admin and the users of the system have a personal HSM where the keys are stored and it works like this:

1. The administrator generates a key inside his HSM with PBKDF2 (random salt and random seed)
2. The HSM of the administrator encrypts the new key using AES-256 with a different symmetric key for each user (the key used for key wrapping was established during the physical initialization of the HSM of the user) and sends it to every user that needs it along with key’s metadata. The whole payload (encrypted key value + key’s metadata) is encrypted another time with AES256 with another unique key for each user.
3. The payload reaches the user that, thanks to the two symmetric keys previously shared with the admin (during the HSM physical initialization), is able to retrieve the requested key and metadata.

I was thinking about another possible approach that could be better but I am not really sure about it:

1. The administrator establishes a shared secret common to every user of the system. This secret is stored in every HSM belonging to the users or to the administrator.
2. When a key must be generated, the administrator computes it with PBKDF2 using the common secret and a random salt.
3. When a key must be sent to any user, only the salt that was used by the administrator is actually sent to the user. The salt may be encrypted with a pre-shared symmetric key (like the example above) and it is used by every user along with the shared secret to generate again the key.

The first approach has the following problems: I need to send the actual key value, I have to perform two encryptions, the HSM must offer an API to retrieve from its internal flash memory the actual value of a key (as cleartext or ciphertext depending on the choice of the caller, the API can be called only if the administrator is logged in the HSM and it can’t be called if the user is logged).

The second approach has the following problems: the secret is common to all users so if an attacker finds the secret of a single user, he founds the secret of everyone. The HSM must offer an API to retrieve the secret as cleartext from its internal flash memory because the secret must be the same for every user, even for users that are added to the system weeks/months later (again this API is callable only if the administrator is logged in the HSM).

I suppose that the second approach, in principle, could be better because the keys are not actually sent from the administrator to the users. But the secret common to everybody is a problem, moreover I imagine that if an attacker finds out the value of a random salt, he may simply try to compute all possible keys given that salt using PBKDF2 and all possible seeds (because the implementation is open source so he knows that the secret is 32 bytes long and he also has access to the PBKDF2 code).

In conclusion I think that in the real world the first approach is more secure, provided that the login as administrator to the HSM is protected by a very complex PIN and possibly by a second factor (i.e. fingerprint). Do you agree? Any thoughts about other vulnerabilities in my approach?

## What is the correct way of grabbing a RANDOM record from a PostgreSQL table, which isn’t painfully slow or not-random?

I always used to do:

SELECT column FROM table ORDER BY random() LIMIT 1;

For large tables, this was unbearably, impossibly slow, to the point of being useless in practice. That’s why I started hunting for more efficient methods. People recommended:

SELECT column FROM table TABLESAMPLE BERNOULLI(1) LIMIT 1;

While fast, it also provides worthless randomness. It appears to always pick the same damn records, so this is also worthless.

I’ve also tried:

SELECT column FROM table TABLESAMPLE BERNOULLI(100) LIMIT 1;

It gives even worse randomness. It picks the same few records every time. This is completely worthless. I need actual randomness.

Why is it apparently so difficult to just pick a random record? Why does it have to grab EVERY record and then sort them (in the first case)? And why do the “TABLESAMPLE” versions just grab the same stupid records all the time? Why aren’t they random whatsoever? Who would ever want to use this “BERNOULLI” stuff when it just picks the same few records over and over? I can’t believe I’m still, after all these years, asking about grabbing a random record… it’s one of the most basic possible queries.

What is the actual command to use for grabbing a random record from a table in PG which isn’t so slow that it takes several full seconds for a decent-sized table?

## How does the random reading part of the divination spell work?

The last section of the diviniation spell reads:

If you cast the spell two or more times before finishing your next long rest, there is a cumulative 25 percent chance for each casting after the first that you get a random reading. The GM makes this roll in secret.

I’m uncertain what this means, what the random reading part specifically means.

## Random disappearance of footer widgets

The footer widget disappear on their own after few days even if the website is untouched. This happened 4-5 times before and I don’t see any security audit log of widget events nor any malware infected. What could be the cause?

There is no solution from the premium theme developers as they have given the common “Added to bug list” reply.

Normal footer:

Footer widgets disappeared:

I have a Development Site for the issue to be checked.

The least security check:

## How to generate a random array satisfying complex constraints

I want to generate several random arrays {x1,x2,x3,x4,x5} that satisfy the following complex constraints:

(2.3 x1 + 4.1 x2 + 2.2 x3 + 3.5 x4 + 1.8 x5  <= 50) && (0 <= x1 <= 5 &&     0 <= x2 && 1 <= x3 <= 5 && 1 <= x4 && 0 <= x5 ) && (2 <= x3 + x4 <= 5)

How I can do it.

## “Brute force” slightly random sha512

I want to test how long it would take someone to run into the hash im using is there a program windows/Linux that can lets me decide the characters used but also put some of the info in. The secret would look like this date %random% hello %random%

They are meant to find the secret given the characters used


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# Mysql – Move ibdata1, set innodb_data_file_path

innodbMySQLmysqldump

I am in a bit of an awkward situation right now. I have a database with a few large InnoDB tables, one of which is about 145 GiB. I have been running a lot of maintenance on this table in particular, not realizing that a lot of that compounded in the ibdata1 file. Now I am in a situation where the ibdata1 file has grown so much that it has used up all of my disk space on my dedicated SQL SSD drive. I have read up on the matter and I know that I have to reload the database into the sql server for it to shrink the ibdata1 file. However, the mysqldump I took of my database is suspiciously small (it is about 2/3rds of my database size and is uncompressed), so what I want to do is load the dump file in a test database to check if there are any issues with it. The issue is, as I do not have any disk space left on my drive (this is a vicious cycle). So, what I would like to do is to move the ibdata1 file to my main HDD, which has plenty of space, and then add a line in the mysql configuration file telling the new location of the ibdata1 file, so I can free up enough space to load up a dummy database. Can I do this? And if so, how do I do this?

Mysql's location; /mysql,
ibdata1 location; /tmpsql/ibdata1 (I can move this to let's say /var/lib/mysql or so if that would be better).

I already set innodb_file_per_table in the configuration file before it used up all my disk space. I have moved the ib_logfile* files as well to the same directory as ibdata1. The ibdata1 file was still used and extended regardless of this setting.

You should be very happy the mysqldump is two-thirds the size of the data. Why?

You should want to move data and indexes without copying unused space at the same time. What aspects would you have to consider by simply importing a mysqldump?

# Aspect #1

InnoDB indexes tend to get very bloaty because Secondary Indexes have keys into the Clustered Index. This always results in a double index lookup. This can be overlooked with large, write-heavy datasets.

# Aspect #2

InnoDB tablespaces tend to get very bloaty because of MVCC being created and discarded without an automatic reclaiming of disk space:

In light of this, you should keep in mind that a mysqldump is a logical representation of the data and indexes. There is no wasted space to be concerned with. You should not have to scp or rsync bloated InnoDB data or logs. Importing a mysqldump into a fresh installation of MySQL should be what you what want.

Once you have loaded the test database with the mysqldump, you should run CHECKSUM TABLE on random tables of various sizes. If all tables have the same checksum value, you could certify as good. Make a disklevel backup of the data on the prod server as well.
• Set innodb_data_file_path=ibdata1:10M:autoextend in /etc/my.cnf

format: plain


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# 11.5: Time Required

Difficulty Level: At Grade Created by: CK-12

Suggested time for each activity is listed in the procedure for each mini-lesson. Anticipated time for complete unit is 2-3 weeks. However, the different sections can be used as stand-alone activities or together to provide a comprehensive water unit.

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Index Theory of Elliptic Operators

Markus Upmeier

Fridays 10:00 - 12:00, April 30 - June 18, 2021
(8 lectures)

Lectures delivered via Microsoft Teams on the Taught Course Centre. Sign up via gradstud@maths.ox.ac.uk for eligible graduate students (Bath, Bristol, Oxford, Warwick, and Imperial).

Lecture notes
Last update: May 29, 2021

Overview and synopsis
Course outline and additional resources
Bibliography

Overview

The Atiyah-Singer index theorem is one of the cornerstones of modern geometry. It relates the number of solutions of elliptic linear differential equations to the topology of the underlying manifold. For a Dirac operator on a spin manifold $M$ acting on $E$-valued spinors the index formula states $$\mathrm{ind}(D_E)=\int_M \widehat{A}(TM)\mathrm{ch}(E).$$ This first half of the lectures will be devoted to explaining the components of this formula, developing the required functional analysis for elliptic differential operators, and providing the topological and geometric background. Then we will sketch a proof and finally discuss some of its many applications, in particular to positive scalar curvature metrics.

Synopsis

Vector bundles, Chern classes, covariant derivatives, Chern-Weil theory; Hirzebruch theory of multiplicative sequences; complex representations of Clifford algebras, spinors; globalization to Riemannian manifolds, spin structures; Dirac operators, other fundamental elliptic operators; pseudo-differential operators and elliptic theory, Fredholm operators; excision proof of the Atiyah-Singer index theorem; applications to positive scalar curvature metrics, generalizations of Rokhlin's theorem.

Prerequisites

Basic knowledge in Differentiable Manifolds, Elementary Topology, Functional Analysis

Course outline

Date Description

April 30 Introduction and overview
Motivation for index theory by explicit examples (torus, circle, projective space); Historical introduction; Dirac's square root of the Laplacian; proof sketch of Hirzebruch signature theorem; applications (Rokhlin, positive scalar curvature)

Literature

[3, Introduction], [4, Introduction], [5, p.120]

May 7 Vector bundles, characteristic classes, and connections
Definition of vector bundle; Transition functions; Connections; Curvature; Invariant polynomials; Chern-Weil homomorphism; Chern classes

Literature

[1, Chapter 1], [12, §2 and Appendix C]

May 14 Genera and multiplicative sequences
Bordism; Multiplicative sequences and their classification; Construction of genera; Examples: Todd, A-genus, L-genus, Chern numbers

Literature

[8, Chapter 1], [9], and [12, §17 and §19]

May 21 Clifford algebras and spinors
Quadratic forms; Definition of Clifford algebra by universal property; Basic examples; Identification with matrix algebras; Spinor representations

Literature

[4, Chapter 1], [11, Chapters 2-3]

May 28 Spin structures and Dirac operators
Principal bundles; Associated vector bundles; Orientations and spin structures; Dirac bundles; Examples of Dirac bundles; Dirac operators and their basic properties

Literature

[10, Chapter II, §1 - §5], [13, Chapters 3 and 4]

June 4 Elliptic theory and the pseudo-differential calculus
June 11 Atiyah-Singer index theorem
June 18 Applications to positive scalar curvature

Bibliography

1
M.F. Atiyah, K-theory, W.A. Benjamin, New York--Amsterdam, 1967.

2
M.F. Atiyah and I.M. Singer, The index of elliptic operators. I, Ann. of Math. 87 (1968), 484–530.

3
D.D. Bleecker and B. Booß-Bavnbek, Index theory—with applications to mathematics and physics, International Press, Somerville, MA 2013.

4
T. Friedrich, Dirac Operators in Riemannian Geometry, Graduate Studies in Mathematics 25, AMS, Providence, RI, 2000.

5
I.M. Gel'fand On elliptic equations Uspehi Mat. Nauk 15 (1960), 113–123.

6
P.B. Gilkey, Invariance theory, the heat equation, and the Atiyah–Singer index theorem, Mathematics Lecture Series 11, Publish or Perish, Inc., Wilmington, DE, 1984.

7
M. Gromov and H.B. Lawson, Positive scalar curvature and the Dirac operator on complete Riemannian manifolds, Inst. Hautes Études Sci. Publ. Math. 58 (1983), 83–196.

8
F. Hirzebruch, Topological methods in algebraic geometry, Classics in Mathematics 131, Springer-Verlag, Berlin, 1995.

9
F. Hirzebruch, T. Berger, and R. Jung, Manifolds and modular forms, E20, Friedr. Vieweg & Sohn, Braunschweig, 1992.

10
H.B. Lawson and M.-L. Michelsohn, Spin geometry, Princeton Mathematical Series 38, Princeton University Press, Princeton, NJ, 1989.

11
E. Meinrenken, Clifford algebras and Lie theory, Ergebnisse der Mathematik und ihrer Grenzgebiete 3, Springer, Heidelberg, 2013.

12
J.W. Milnor and J.D. Stasheff, Characteristic classes, Annals of Mathematics Studies 76, Princeton University Press, Princeton, N. J., 1974.

13
J. Roe, Elliptic operators, topology and asymptotic methods, Pitman Research Notes in Mathematics Series 395, Second Edition, Longman, Harlow, 1998.


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# Representations versus (g,K) modules

Let $G$ be a connected semisimple Lie group with finite center. Let $(\pi,V)$ be an admissible representation on a Banach space $V$. Is it true that the following are equivalent?

(a) $\pi$ is irreducible

(b) the $({\mathfrak g},K)$-module of $K$-finite vectors is simple.

I can prove this for unitary representations. If the answer is positive, where do I find a simple proof? Say, a proof that does not use the classification of admissible $({\mathfrak g},K)$-modules?

After some thinking, I realised that my solution for the unitary case also works in general. The difficult direction is (a)$\Rightarrow$(b): Let $K$ be a maximal compact subgroup and let $V_K$ denote the space of $K$-finite vectors. and let $0\ne U\subset V_K$ be a $({\mathfrak g},K)$-submodule. Let $V^\omega$ denote the space of analytic vectors, which is dense in $V$. After projection, the space $V^\omega(\tau)=V^\omega\cap V(\tau)$ is dense in the $K$-isotype $V(\tau)$ for any $\tau\in\widehat K$. Since $V(\tau)$ is finite-dimensional by admissibility, we get that every $K$-finite vector is analytic. Hence for given $u\in U$ and $X\in\mathfrak g$ the curve $\gamma:t\mapsto \pi(\exp(tX))u$ is analytic. It satisfies $\gamma^{(n)}(0)=\pi(X)^nu\in U\subset\overline U$ for every $n\ge 0$. As $\gamma(t)=\sum_{n=0}^\infty\gamma^{(n)}(0)t^n/n!$ for small $t$, it follows that $\pi(g)u\in \overline U$ for all $g$ in some small unit-neighborhood in $G$. By continuity it follows $\pi(g)\overline U\subset \overline U$ for every $g$ in that unit-neighborhood and as this unit-neighborhood generates $G$, we get that $\pi(G)$ preserves $\overline U$. By irreducibility, $\overline U=V$ and so, by finite-dimensionality of the $K$-type $V(\tau)$ we have $V(\tau)=\overline U(\tau)=U(\tau)$, so $U=V_K$.


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# 29 May 2019: UPSC Exam Comprehensive News Analysis

A. GS1 Related
GEOGRAPHY
1. Scientists give the thumbs-up for Anthropocene epoch
SOCIAL ISSUES
1. HC seeks Centre’s response on plea for raising abortion time period
B. GS2 Related
POLITY AND GOVERNANCE
1. Karnataka ordered to release 9.19 tmcft
2. Petition in High Court to tackle population growth
INTERNATIONAL RELATIONS
1. Sri Lanka, Japan & India sign deal to develop container terminal
C. GS3 Related
ENVIRONMENT AND ECOLOGY
1. Ozone pollution likely to spike in Capital
D. GS4 Related
E. Editorials
ECONOMY
1. The key agenda must be to accelerate growth
2. A ‘social’ index for Ease of Doing Business
3. In his second term, Modi can ensure better urbanisation through greater devolution of power, and finances
F. Tidbits
1. Burnout is not a medical condition
G. Prelims Facts
H. UPSC Prelims Practice Questions
I. UPSC Mains Practice Questions

A. GS1 Related

1. Scientists give the thumbs-up for Anthropocene epoch

Context:

A 34-member panel of the Anthropocene Working Group (AWG) voted 29-4 in favour of designating a new geological epoch — the Anthropocene.

Holocene:

• The current epoch is the Holocene.
• It is about 11,700 years of stable climate since the last ice age during which all human civilisation developed.
• As Earth entered a warming trend, the glaciers of the late Paleolithic retreated. Tundra gave way to forest.
• As the climate changed, the very large mammals that had adapted to extreme cold, like mammoth and wooly rhinoceros, became extinct.
• Humans, once dependent on these “mega mammals” for much of their food, switched to smaller game and increased their gathering of plant materials to supplement their diet.
• Evidence indicates that about 10,800 years ago, the climate underwent a sharp cold turn lasting for several years.
• As temperatures began to rebound, human population began to increase and we began inventing the processes that would change the planet forever.
• The Holocene and the preceding Pleistocene together form the Quaternary period.

Anthropocene:

• The term ‘Anthropocene’ was coined in 2000 by Nobel Laureate Paul Crutzen and Eugene Stoermer to denote the present geological time interval in which human activity has profoundly altered many conditions and processes on Earth.
• According to the AWG, the phenomena associated with the Anthropocene include
• An order-of-magnitude increase in erosion and sediment transport associated with urbanisation and agriculture
• Marked and abrupt anthropogenic perturbations of the cycles of elements such as carbon
• Environmental changes generated by these perturbations including global warming, sea-level rise, and ocean acidification
• Rapid changes in the biosphere
• Proliferation and global dispersion of many new minerals, rocks including concrete, fly ash, plastics, and the myriad ‘technofossils’ produced from these materials.
• The most recent period of the Anthropocene has been referred to by several authors as the Great Acceleration during which the socioeconomic and earth system trends are increasing dramatically, especially after the Second World War. For instance, the Geological Society termed the year 1945 as The Great Acceleration.

Details:

• The panel plans to submit a formal proposal for the new epoch by 2021 to the International Commission on Stratigraphy
• The International Commission on Stratigraphy is responsible for deciding and defining the divisions of geological time.
• The focus is now on identifying a definitive geologic marker or golden spike (technically called Global boundary Stratotype Section and Point) to signal the beginning of the Anthropocene Epoch.
• The golden spike must be present globally and should be a part of deposits for geological record.
• Many in the AWG believe that artificial radionuclides spread across the world by atomic bomb tests from the early 1950s would serve as the golden spike. The radionuclides are present almost everywhere from marine sediments to ice layers and even stalagmites and stalactites.
• Once a formal proposal is made by the AWG, it will be considered by several more groups of the International Commission on Stratigraphy.
• The final ratification will be made by the executive committee of the International Union of Geological Sciences.

1. HC seeks Centre’s response on plea for raising abortion time period

Context:

The Delhi High Court issued notice to the Centre on a petition seeking to raise the time period for terminating pregnancy in case of health risk to the mother or the foetus from the current cap of 20 weeks to 24-26 weeks.

Medical Termination of Pregnancy Act 1971:

• MTP Act allows women to go through abortions up to 20 weeks. For cases beyond the current time period, permission of a High Court is required.
• However, courts can make exceptions if abnormalities are detected and if there is a substantial risk to the mother’s life and health. A pending bill in Parliament proposes to amend the MTP Act to extend it to 24 weeks.
• MTP Act, 1971 is totally silent about termination of pregnancy of unmarried females and widows but it makes termination of pregnancy as an offence punishable under Indian Penal Code if the same is not done in accordance with the Act.

Issue:

• Medical Termination of Pregnancy (MTP) Act, 1971 completely prohibits termination of pregnancy in case foetus is suffering from severe abnormality even after a period of 20 weeks.
• The foetal abnormalities are detected appropriately between 18 to 20 weeks and the period of one-two weeks is too small for the would-be parents to take the difficult call on whether to keep their baby or to abort the same.
• Even if the foetus is scanned and found positive with serious abnormalities, the woman is forced to carry pregnancy due to bar provided under MTP Act.
• The abortion beyond a period of 20 weeks is permitted only if continuing the pregnancy poses a substantial risk to the woman’s life. But the law does not take care the factum of serious abnormalities suffered by the child in the womb and detected after 20th week.
• The lack of legal approval moves abortion to underground [illegal manner] and they are done in unhygienic conditions by untrained persons, thus putting thousands of women at risk.
• MTP Act, 1971 is totally silent about termination of pregnancy of unmarried females and widows but it makes termination of pregnancy as an offence punishable under Indian Penal Code if the same is not done in accordance with the Act.

Abortion laws in other countries:

• Many European countries, including France, U.K. and Italy and even neighbouring country Nepal allow abortion after 20 weeks if foetal abnormalities are discovered.
• Twenty-three countries, including Canada, Germany and Vietnam, allow abortion at any time if the request is based on social or medical reasons.

Details:

• Responses were sought from the Health and Law Ministries, and the National Commission for Women on the plea.
• The petition filed by social activist and advocate has contended that unmarried females and widows too should be allowed to undergo a legal abortion.
• It has pleaded the court to hold that the right to abort the pregnancy is a fundamental right of the woman’s body sovereignty and each woman has the sole right to make decision about her body in the context of carrying such pregnancy or to terminate the same, subject to checks as provided under the MTP Act or further checks, which may be provided.
• The plea has also sought directions to deal with cases pertaining to termination of pregnancy where anomaly is detected after 16 weeks on fast track basis under MTP Rules to ensure that woman must not suffer due to administrative delay in taking decision or giving consent for termination of pregnancy.
• The Supreme Court, in 2017, had declined to amend the Act which prohibits termination of pregnancy beyond 20 weeks, saying that the issue fell within the legislative realm.

B. GS2 Related

1. Karnataka ordered to release 9.19 tmcft

Context:

The Cauvery Water Management Authority (CWMA) has ordered Karnataka to release 9.19 tmcft of water for the month of June from the Biligundlu reservoir to the Mettur Dam in Tamil Nadu.

River Cauvery:

• River rises on Brahmagiri Hill of the Western Ghats in south-western Karnataka state. It flows in a south-easterly direction through the states of Karnataka and Tamil Nadu.
• Before emptying into the Bay of Bengal the river breaks into a large number of distributaries forming a wide delta.
• Its main tributaries are the Kabani, Amaravati, Noyil, and Bhavani rivers.
• The river, upon Upon entering Tamil Nadu, continues through a series of twisted wild gorges until it reaches Hogenakal Falls. There the Mettur Dam has been constructed for irrigation and hydel power.

Background:

• The sharing of waters of River Cauvery has been the source of a serious conflict between the two states of Tamil Nadu and Karnataka. The genesis of this conflict rests in two agreements in 1892 and 1924 between the Madras Presidency and Kingdom of Mysore.
• Central Government, in exercise of the powers conferred by section 4 of the Inter-State River Water Disputes Act, 1956 had constituted the Cauvery Water Disputes Tribunal to adjudicate upon the water dispute regarding the Inter-State river Cauvery and the river valley thereof among the States of Karnataka, Kerala, Tamil Nadu and Union territory of Puducherry.
• Subsequently, in exercise of the powers conferred by section 6A of the Inter-State River Water Dispute Act, the Central Government notified the Cauvery Water Management Scheme on 01st june, 2018.
• It further constituted the ‘Cauvery Water Management Authority’ and the ‘Cauvery Water Regulation Committee’ to give effect to the decision of the Cauvery Water Disputes Tribunal as modified by Supreme Court through its Order, dated 16th February, 2018
• In the same order, the Supreme Court had recognised the principle of equitable distribution of inter-State rivers.

Details:

• Representatives from all riparian States attended the CWMA meeting.
• This is the third meeting of the CWMA since June 2018, when it was first constituted, and it is expected to meet once in 10 days from June to October.

2. Petition in High Court to tackle population growth

Context:

A petition moved before the Delhi High Court has sought directions to the government to set ‘two-child norm’ as criteria for government jobs, aids and subsidies, to control the country’s rising population.

Details:

• The petition has also sought implementation of the recommendations for population control made by the National Commission to Review the Working of the Constitution (NCRWC) headed by Justice Venkatchaliah.
• It appeals that The non-compliance of the norm should lead to the withdrawal of citizens statutory rights including the right to vote and contest elections
• The petitioner claimed that India’s population has marched ahead of China, as about 20% of the population does not have Aadhaar and therefore, is not accounted for, and there are also crores of Rohingyas and Bangladeshis living illegally in the country.
• He additionally claimed that “population explosion is also the root cause of corruption”, apart from being a contributory factor behind heinous crimes like rapes, domestic violence, etc.
• It was also claimed that without population control, campaigns like Clean India and Save the Girl Child would not succeed.
• The two-child norm for contesting local body elections has been adopted by states like Andhra Pradesh, Gujarat, Maharashtra, Odisha, Rajasthan and Haryana has yielded very positive results in reducing the population growth in those states.
• The appeal argues that even though India was the first country in the world to have a population policy, it has not achieved much in terms of population control due to the negligence of the governments.

National Commission to Review the Working of the Constitution (NCRWC):

• The National Commission to review the working of the Constitution (NCRWC) also known as Justice Manepalli Narayana Rao Venkatachaliah Commission was set up by a resolution of the  Government of India led by Atal Bihari Vajpayee on 22 February 2000 for suggesting possible amendments to the Constitution of India.
• It submitted its report in 2002.
• The terms of reference given to the Commission stated that the Commission shall examine, in the light of the experience of the past fifty years, as to how best the Constitution can respond to the changing needs of efficient, smooth and effective system of governance and socio-economic development of modern India within the framework of parliamentary democracy, and to recommend changes, if any, that are required in the provisions of the Constitution without interfering with its ‘basic structure’ or ‘basic features’.

1. Sri Lanka, Japan & India sign deal to develop container terminal

Context:

Sri Lanka, Japan and India signed an agreement to jointly develop the East Container Terminal at the Colombo Port.

Details:

• The joint initiative is estimated to cost between $500 million and$700 million.
• As per the agreement signed the Sri Lanka Ports Authority (SLPA) retains 100% ownership of the East Container Terminal (ECT), while the Terminal Operations Company, conducting its operations, is jointly owned, the SLPA said in a statement.
• Sri Lanka will hold a 51 per cent-stake in the project and the joint venture partners will retain 49%.
• Japan is likely to provide a 40-year soft loan with a 0.1 percent interest rate.
• Japan also had helped development of the Jaya Container Terminal at the Colombo Port, supporting its operations since the 1980s.

Significance:

• The signing of the Memorandum of Cooperation (MoC) is significant, given that the countries had been negotiating the deal since last year, with little success.
• Last year, India’s possible role in developing the terminal had become a major flashpoint within the government.
• President Maithripala Sirisena had opposed any Indian involvement in the project, as roping in foreign actors for developing “national assets” remains a politically sensitive call in the island, especially among nationalist trade unions.
• India and the United States are both concerned that a Chinese foothold at Hambantota, south of Colombo, could give it a military naval advantage in the Indian Ocean.
• Sri Lanka has insisted that its ports will not be used for any military purposes.
• The ECT for which India has now entered into an agreement is located 3 km away from the China-backed international financial city, known popularly as “port city”, being built on reclaimed land on Colombo’s sea front.

C. GS3 Related

1. Ozone pollution likely to spike in Capital

Context:

With rising temperatures, surface ozone pollution is expected to increase in Delhi in the next three days, according to a forecast by the System of Air Quality and Weather Forecasting and Research (SAFAR).

Details:

• Surface ozone can lead to cough, shortness of breath, throat pain in short term and cause corrosion of linings of lungs and make lungs vulnerable to further infections in case of long-term exposure.
• For people who already have lung and respiratory diseases, it would be further aggravated.
• Maximum temperatures are likely to rise gradually by 2-3 degrees Celsius during the next three days which will increase the production of surface ozone.

What is surface ozone?

• Surface ozone is not a primary pollutant and it is produced due to chemical reactions of NOx (nitrogen oxides), CO (carbon monoxide) in the presence of sunlight.
• When temperature increases, the rate of production of ozone also increases.
• It can cause fatigue, breathlessness, and asthma.

SAFAR:

• SAFAR stands for the state of art Air Quality and Weather Forecast system.
• The giant true colour LED display gives out real-time air quality index on 24×7 basis with colour coding along with 72-hour advance forecast.
• Based on the Air Quality Index on a particular day, health advisory and related precaution will be notified to prepare citizens well in advance.
• The system is first of its kind in India and is the most advanced system. It is installed at Chandni Chowk in Delhi.
• SAFAR is operationalized by the Indian Meteorological Department (IMD). It was indigenously developed by the Indian Institute of Tropical Meteorology.
• In addition to regular air quality and weather parameters like Carbon Monoxide, Particulate Matter -PM2.5, PM10, Nitrogen Oxides, Sulfur Dioxide and Ozone, it will measure Black carbon, Mercury, sun’s UV-Index (UVI) and PM1 in real time.
• It can also provide the measurement of online automatic ultrafine particles Mercury and PM1, both of which have direct relevance to human health.
• It will also monitor the existence harmful pollutants of Xylene, Toluene and Benzene.

D. GS4 Related

Nothing here for today!!!

E. Editorials

1. The key agenda must be to accelerate growth

#### Editorial Analysis:

• Experts have opined that now that the general election is over, the time has come to pay serious attention to the economy.
• As a matter of fact, the national income numbers continue to be controversial.
• It is important to note that no serious policy decision can be taken with ambiguous numbers. Nevertheless, even with the new official numbers it is clear that growth is slowing down.
• As in the revised new base estimates, the growth rate in 2016-17 was 8.2%; in 2018-19 it was 7%. Accelerating economic growth must be on top of the agenda of the new government.
• It is only a fast growing economy that will generate the surpluses which are necessary to address many of our socio-economic problems and to provide social safety nets.

A decline in investment rate:

• For faster growth, what is critically needed is a higher investment rate.
• In current prices, the ratio of Gross Fixed Capital Formation to Gross Domestic Product has stayed low at 28.5% between 2015-16 and 2017-18.
• Further, in 2018-19 it is estimated at 28.9%. In 2007-08, it was as high as 35.8%. In constant prices, the ratio, has, however, shown a smaller decline from the peak.
• It is true that for a time growth can come out of better utilisation of existing capacity. But for sustained growth, the ratio has to go up, and that too substantially.
• Further, there are several studies which indicate a fall in corporate investment. Every year the Reserve Bank of India (RBI) publishes a forecast of corporate investment.
• It uses the data made available by banks and other financial institutions on the phasing of capital expenditures of projects sanctioned by them.
• As a matter of fact, an article in the March 2019 issue of the RBI Bulletin says that in 2017-18, the capital expenditures of the corporate sector were estimated at ₹1,487 billion.
• There has been a steady decline from ₹2,050 billion in 2014-15.
• The industry-wise distribution of projects sanctioned by banks and other institutions in 2017-18 shows that the power sector accounted for 38.2% of the total expenditure. Pure manufacturing had only a small share.
• Experts opine that all these point to the urgent need to accelerate investment.

Case on Reviving investment:

• Firstly, much of public investment happens outside the Budget.
• In 2019-20, capital expenditures of the Central government to GDP are expected to be 1.6%.
• This ratio has not shown much change.
• It is important to note that the bulk of public investment comes from public sector enterprises, including the Railways.
• What is needed is for the government to interact with all public sector units and prepare a programme of public investment for 2019-20.
• As a matter of fact, public sector units can take a longer-term view than the private sector.
• A strong public investment programme can be a catalyst of private investment.
• In a situation such as the present one, it can crowd in private investment.
• Secondly, there has to be sector- or industry-wise discussions between the government and industrialists to understand the bottlenecks that each industry faces in making investment and take actions to remove them.
• Currently, banks are under stress and the ratio of non-performing assets (NPAs) has risen.
• Experts opine that this needs to be resolved as early as possible so that banks can get back to lending at a significant pace. In the absence of term lending financial institutions, banks provide both working capital and long-term loans.
• That is why resolving the issue of NPAs is critically important for larger flow of long-term funds. Further, the government must also infuse adequate capital into banks at one go.
• As a matter of fact, there are mechanisms such as resolution councils or committees which can help to resolve the NPA problem without the bank management coming under scrutiny of investigative agencies.
• Over the medium term, experts opine that one can consider reviving the setting up of separate long-term financial institutions, partly funded by government.

Perspective on Jobs and growth:

a. Growth: An answer to the problem of jobs

• There has been great concern about the inability of the economy to generate adequate employment.
• As a matter of fact, employment numbers have always been somewhat worrisome because of the presence of heavy underemployment in the country.
• Perhaps there has been some shift of employment from the unorganised to the organised segment. But this does not alter the overall situation.
• It is important to note that the answer to the problem of jobs is only growth.
• It is faster growth and faster investment which will generate employment.

b. The pattern of growth

• Of course the pattern of growth also counts.
• Some sectors such as construction are more labour intensive.
• Sectors such as IT and the financial system, which provided attractive employment to young educated entrants to the labour market in the past, have their own problems.
• However, an improvement in the financial system may trigger some new jobs.
• Ultimately, it is overall growth which is key to more employment.
• Further, it is generally argued that growth will happen only if there is an adequate increase in demand.
• While this is true in relation to some sectors, there are many sectors including infrastructure where new investment will spur growth.

c. Agrarian Distress

• In this context, the main concern is the slowdown in rural demand, which can affect the off-take of consumer goods.
• Agrarian distress, which is the cause of slowdown in demand, needs to be tackled on a priority. It is important to note that where distress is due to a fall in prices, the best course of action is to resort to limited procurement so that the excess over normal is procured by the government.
• Further, as far as increase in agricultural output in the short run is concerned, the monsoon is a big question mark.
• Nothing can be done about it except changing the cropping pattern depending on rainfall.
• However, making available inputs such as seeds and fertilizers at an affordable cost must be the major task particularly of State governments.

d. Looking at the Medium Term:

• Next, over the medium term, more attention must be paid to increasing agricultural productivity through consolidation of land holdings and spreading better techniques of cultivation.
• As a matter of fact, improving marketing arrangements has been a neglected area.
• Coming to the medium term, reforms have been moving in the right direction.
• The introduction of the Goods and Services Tax is a major step.
• However, glitches still remain in its implementation.
• Experts opine that the government should get tax authorities, industrialists, traders and, particularly, exporters to sort out the issues together.
• The Insolvency and Bankruptcy Code was another significant step taken in the last few years.
• Even here there are some bottlenecks and the government must address them.

e. Land and Labour Reforms:

• Land reforms which enable entrepreneurs to buy land speedily have been suggested.
• Some steps in this regard have been taken in the past.
• It is important to note that compulsory acquisition of land is the antithesis of competition and should be resorted to only in limited cases where public interest is involved.
• Experts also opine that labour reforms should wait until the economy has picked up steam and moved to a higher growth path.

Concluding Remarks:

• Lastly, in the wake of electioneering, there was a lot of talk on social safety nets, more so on providing a minimum income to the poor.
• It is important to note that any caring society should do this. But it also depends on the ability of the government to sustain it.
• Experts opine that the government should move in the direction of removing some of the subsidies and schemes which are similar in nature to minimum income, consolidate them, add to them what is fiscally feasible and provide the funds directly to the poor.
• Having said this, the bigger problem is to define the ‘poor’ and, more particularly, identify them. But a move in this direction must be part of the agenda.
• To conclude, besides economic factors, non-economic factors are also critically important to revive what are often described as ‘animal spirits’.
• Investment today is based on expectations of future earnings.
• Thus it is an act of faith in the future. For this to happen, there must be social and political tranquility.

2. A ‘social’ index for Ease of Doing Business

#### Note to the Students:

• This analysis is taken from an article published in the Hindu Business Line on the 29th of May, 2019.

#### Editorial Analysis:

• Experts opine that the Modi government promoted “competitive federalism” among States through its “Make in India” initiative, to improve the nation’s rank in the World Bank’s Ease of Doing Business (EoDB) ranking.
• As a matter of fact, the initial recommendations from the PMO on 98 reform measures in 2014, based on the 10 business topics tracked and monitored by the World Bank’s doing business report, was later extended to 340 points encompassing a Business Reform Action Plan (BRAP) for the States.
• This was construed as pertaining to “58 regulatory processes spread across 10 reform areas that cover lifecycle of a business”.
• There are two clear concerns against this. These are as follows:
1. Firstly, it is uncertain whether such indicators that essentially call for reducing the “transaction costs” from the governance perspective adequately capture the on-ground conditions of doing business, as has been pointed out by a recent publication by the Asia Competitiveness Institute (ACI), National University of Singapore.
2. Secondly, in no way, can these conditions adequately represent the overall business environment that can woo investors: these reflect very few partial conditions. History and political environments have a massive bearing on business environment.

Beyond the World Bank:

• Experts opine that the EoDB, as per the World Bank definition, is reductionist, and in no way, a true reflection of ground reality.
• This position has also been taken by the ACI, who have come up with their own index on ease of doing business on the basis of three broad parameters: Attractiveness to Investors, Business Friendliness, and Competitiveness Policies. This is definitely a substantial improvement over the World Bank’s one!
• Further, on-going research suggests that the States should concentrate on the UN Sustainable Development Goals (SDG) as major enablers of business competitiveness.
• With this hypothesis in mind, some experts have developed an SDG index for 23 States.
• This is a weighted index considering 14 of the 17 SDGs based on 76 indicator variables’ normalised values.
• These 14 goals reflect the status of SDGs’ achievement in States by taking into account parameters that are characteristic of the socio-economic fabric of the nation.
• This is a clear improvement over the one developed by the NITI Aayog on two grounds:

(a) the “ad-hoc”-ness in weight determination of the component indicators has been removed through statistical methods like principal component analysis,

(b) the crucial ‘climate action’ goal, blatantly neglected by the NITI Aayog, has been incorporated in this index. The ranks of the States are given in the accompanying table.

• Further, there is a two-way causality between business performance and SDGs.
• This is because SDGs address the input and product market conditions through bolstering the potentially available capital classified in four types, namely, physical capital, natural capital, social capital and human capital, which are critical inputs to businesses to thrive.
• Also, almost all the SDGs are embedded in one form of capital or the other, i.e.,
1. human (SDGs 1 – 5: reflecting on poverty, hunger, health, education, and gender equality),
2. physical (SDGs 8 and 9: employment, growth, industry, innovation and infrastructure),
3. natural (SDGs 14 and 15: life below water and land respectively) and
4. social (SDGs 10 and 16: social institutional variables etc).
1. Econometric analysis by experts show that this newly devised SDG index, is a statistically significant causal variable explaining the Ease-of-Doing-Business Index, as developed by the Asian Competitiveness Institute (ACI).
2. As a matter of fact, one also finds a significant causal relation between this index and per capita Foreign Direct Investment (FDI) in the States, indicating that financial capital gets drawn towards those destinations where enabling business conditions are already created through prevalence of the four types of capital.
• The above argument buttresses the contention that SDGs should be treated as important cornerstones of “competitive federalism” in the Indian context, rather than the World Bank metric of EoDB.
• This is from two perspectives:
1. The first is from the perspective of attracting businesses and financial capital.
2. The second is from the perspective of looking at development bringing in the efficiency, equity, and sustainability concerns in one frame.

3. In his second term, Modi can ensure better urbanisation through greater devolution of power, and finances

#### Note to the Students:

• This analysis is taken from an article published in the Indian Express on the 29th of May, 2019.

#### Editorial Analysis:

• It is important to note that State governments have the principal responsibility for urban development.
• However, in order to deliver, they can and should ensure that city governments are sufficiently empowered to get the job done.
• The state governments need to decentralise, devolve and empower the cities.
• As Prime Minister Narendra Modi begins his second term with an even larger political mandate, it is time to reflect on what should be the priorities in fixing our cities.

Examining the priorities in fixing our cities:

• The scale of the challenge is massive whether we look at the availability of clean drinking water, unpolluted air, quality of public transport, traffic management and parking, integrated planning of transport and land use, law and order, management and safe disposal of solid waste that is generated, treatment of waste water and effluents, and affordable housing.
• As a matter of fact, in short, the state of public service delivery in our cities is abysmal and what is more, the cities are financially broke and cannot address these problems on their own.
• It is also important to note that rapid economic growth in any country is associated with a decline in the share of agriculture and increase in the shares of manufacturing and services in its GDP, and this involves greater urbanisation.
• As a matter of fact, India’s experience in the last two decades has been no different, except that the urbanisation associated with rapid growth has been largely unplanned, much more so than in most other developing countries aspiring to middle-income status.
• Experts opine that going forward, as we try to achieve rapid growth which is necessary to provide growing employment opportunities for our young work-force, we need to position our cities as drivers of the structural transformation of the Indian economy.

A Look at some projections:

• UN projections suggest that India’s urban population will increase from 461 million in 2018 to 877 million in 2050, with India contributing the largest share of global urban population growth from 2018 to 2050.
• Next, Indian cities will have to provide a much better quality of life if we want to create a climate which will attract investment.
• For this, we not only need more and better urban infrastructure but also significantly better institutions, which can manage the infrastructure and deliver public services of high quality.
• State governments have the principal responsibility for urban development.
• However, in order to deliver, they can and should ensure that city governments are sufficiently empowered to get the job done.
• This requires strengthening the finances of these governments, building their capacity to take on the new challenges that urbanisation brings, and providing an enabling environment through legislative and administrative support. Unfortunately, most state governments have been failing in this respect.

Powers that State Governments have:

• In our federal system, a state government has the power to notify when an area is to have a statutory urban local government and what form it would take — a municipal corporation, a municipal council or a nagar panchayat (when an area is in transition from rural to urban).
• Further, the 74th Constitutional Amendment of 1992 gives the state governments the power to transfer a set of 18 legitimate municipal functions to the municipal governments and also devolve finances to them to enable them to perform these functions and organise the delivery of the public services.
• It is important to note that State governments were happy to devolve most, though not all, of the 18 functions to the urban local governments. Town planning — the golden goose — was not typically transferred. Also, action on the devolution of funds to urban local governments has been unpredictable and hopelessly inadequate.
• As one municipal commissioner put it to me, “We do not function as city governments but as urban local bodies. We are accountable to our residents for service delivery but we are not empowered to deliver the services”. State governments have to accept this failure and take corrective action.

Local Governments: Lack of Financial Devolution

• Experts opine that a major opportunity to improve municipal finances was lost at the time of the GST-related constitutional amendments in 2016.
• In moving to a more efficient GST regime, the Centre and the states agreed that GST would be a dual levy on a common base by subsuming most of the consumption taxes imposed by the Centre, states and local governments.
• Ideally, they should have agreed that GST revenue should be shared among all the three levels of government, since the independent power of local governments to raise their own sources of revenue has now been appropriated by the Centre and states.
• However, the third tier was kept out of the deal.
• This is in contrast with many countries around the world which have provided their urban local governments, access to revenue from goods and services tax and income tax.
• Experts opine that the Government of India must work towards amending the Constitution to undo the injustice that has been meted out to local governments.
• In fiscal devolution, the talk of cooperative federalism stops at the level of the state government.
• Over the years, the state governments have claimed and successfully obtained a larger share in the joint revenues of the Centre and the states.
• The Fourteenth Finance Commission increased the share of states in the revenue pool from 32 per cent to 42 per cent.
• By contrast, municipal revenues/expenditures in India have been stagnating at around 1 per cent of GDP for over a decade.
• This is much lower, for example, than the municipal revenues/expenditures in Brazil which account for 7.4 per cent of GDP and 6 per cent in South Africa.
• Further, the 15th Finance Commission has an opportunity to prescribe grants from the Centre to the urban local governments.

Recognizing Urbanization as a means to accelerate India’s Growth:

• In the past decade or so, the Centre has come to recognise that urbanisation is set to accelerate with India’s rapid growth.
• Firstly, the UPA government launched the Jawaharlal Nehru National Urban Renewal Mission (JNNURM) and Rajiv Awas Yojana as centrally sponsored schemes.
• The NDA government followed up with a number of their own urban development missions like Swachh Bharat, AMRUT, Smart Cities Mission, and Housing for All.
• Experts opine that these national initiatives have provided some finance and also nudged the state governments to take up the challenges of urban development, and all this made some difference.
• An important point to note is that the national missions could deliver only where the state governments were pro-active in bringing about the change.
• Further, while being aspirational and providing strategic leadership, these missions put forth only limited funds and rightly expected the state governments to raise the rest by either mobilising their own financial resources or by attracting public-private partnerships.
• Only a few state governments have been able to come forward to realise the potential offered by the national missions.
• The missions played an additional role in igniting a competitive spirit among the state governments in the delivery of public services.

Concluding Remarks:

• A major failing of the national missions has been that they have not addressed the issues of empowerment and devolution to the third tier.
• A simple solution would be for the Government of India to introduce an incentive grant system whereby states which devolve funds to some desired degree get to top up the financial grant from the Centre.
• This should be limited to second-tier cities, which are crucial to a new urbanisation thrust. Metropolitan cities need such grants much less, since states can help them raise resources by empowering them to unlock land value.
• They are also better placed to develop PPPs with viable revenue models to attract private funds.
• Prime Minister Modi at the present juncture is in a unique position of having to work with a large number of BJP-controlled state governments. It is a valuable opportunity to grasp the bull by the horns politically, and get the states to go for empowerment of the third tier and also strengthen their finances through assured devolution.
• In conclusion, essentially, co-operative federalism needs to go deeper, below the state level. There are no shortcuts to improving the state of our cities.
• The state governments need to decentralise, devolve and empower the cities.
• We, as responsible citizens, need to engage with the government to find collective solutions while at the same time, holding the government accountable.

F. Tidbits

1. Burnout is not a medical condition

• The World Health Organization said that “burnout” remains an “occupational phenomenon” that could lead someone to seek care but it is not considered a medical condition.
• The clarification came a day after the WHO mistakenly said it had listed burnout in its International Classification of Diseases (ICD) for the first time.
• The World Health Assembly, WHO’s main annual meeting approved the latest catalogue of diseases and injuries, collectively known as the ICD-11.
• While burnout was listed in the previous version, the ICD-10, its definition has been changed in the latest edition of the text.
• WHO has now defined burnout as “a syndrome conceptualised as resulting from chronic workplace stress that has not been successfully managed”.
• It said the syndrome was characterised by:

1) Feelings of energy depletion or exhaustion.

2) Increased mental distance from one’s job, or feelings of negativism or cynicism related to one’s job.

3) Reduced professional efficacy.

• The updated ICD list was drafted last year following recommendations from health experts around the world.
• The ICD-11, which is to take effect in January 2022, contains several other additions, including classification of “compulsive sexual behaviour” as a mental disorder.
• It does for the first time recognise video gaming as an addiction, listing it alongside gambling and drugs like cocaine.
• The updated list removes transgenderism from its list of mental disorders, listing it instead under the chapter on “conditions related to sexual health”.

G. Prelims Facts

Nothing here for today!!!

H. Practice Questions for UPSC Prelims Exam

Q1. Consider the following statements:
1. System of Air Quality and Weather Forecasting gives out real-time air quality index.
2. It was indigenously developed by ISRO.
3. It monitors the existence harmful pollutants of Xylene, Toluene and Benzene.

Which of the given statement/s is/are correct?

a. 1 and 2 only
b. 2 and 3 only
c. 1 and 3 only
d. 1, 2 and 3

See
Q2. Consider the following statements:
1. Network For Spectrum (NFS) is a project related to the network for defence services.
2. It is being implemented by DRDO.

Which of the given statement/s is/are correct?

a. 1 only
b. 2 only
c. Both 1 and 2
d. Neither 1 nor 2

See
Q3. Consider the following statements about Vinaya Pitaka
1. Tripitaka was compiled by Buddha.
2. Vinaya Pitaka comprises the collection of rules given to the community of Buddhist believers.

Which of the given statement/s is/are correct?

a. 1 only
b. 2 only
c. Both 1 and 2
d. Neither 1 nor 2

See


text:
# ECET210 Wk 7 Homework

This is a Regulated DC Power Supply design problem. The students must choose the values of the following parameters for the design:

VOut = 6.0 V or 10.0 V or 12.0 V

RL = ?? Ω and R1 = ?? Ω

Wattage ratings of R1 and RL to be determined

IL = 20 mA; IZD = 20 mA; IR1 = ?? mA

Voltage VA_DC = VB + 3 V

Turns ratio, n = ??

Pick an output voltage number from (a)

Choose the appropriate Zener Diode from the data sheet given below.

Determine the Ω values and the wattage ratings of R1 and RL.

Determine the peak value of the transformer secondary voltage VS.

Determine the transformer turns ratio n.

Assume the following:

Rectifier diode drop = 0.7 V for each. The DC Voltage (after smoothing by the capacitor) is equal to the peak value of the peak value of the full wave rectified pulses.

The Zener voltages are the Nominal Values

a) we choose $Vout = 12 V$

The nominal regulated voltage of the zener diode is 12 V. From the attached table the diode is 1N5242B.

b) from $Il =20 mA$ it results $RL = Vout/IL =12/0.02 =600 ohm$

The internal resistance of the voltage source (need to be at least 10 times smaller than the resistance of the load.

$R1 =RL/10 =600/10 =60 ohm$

d) $IR1 = IL + Izd = 20+20 =40 mA$

c) the power on a resistor is $P = I^2*R$

$P(RL) = 0.02^2*600 = 0.24 W$

$P(R1) =0.04^4*60 = 0.096 W$

e) $V(A_DC) = Vout +I1*R1 = 12 +0.04*60 = 14.4 V$

$V(A_DC) = V(S) + 3V$

3 V is the voltage loss on the bridge rectifiers $0.7*4 =2.8 V$

$V(S) = 14.4 – 3 = 11.4 V$

Since V(A_DC) is equal to the peak voltage of the bridge rectifier it implies that $V(S) = 11.4 V$ is the peak value.

f) V(S) is the peak value.

The peak value for V(primary) is

$V(primary) = V(RMS)*sqrt{(2)} =120*sqrt{(2)} = 169.7 V$

The transformer turns ratio is

$n = V(primary)/V(S) =169.7/11.4 = 14.72$


text:
# On the solvability group

Let $$G$$ and $$H$$ be two groups such that

1. $$|G|=|H|$$;
2. for every natural number $$n$$ the number of elements of order $$n$$ in $$G$$ and $$H$$ are equal;
3. $$H$$ is a solvable group.

Is $$G$$ solvable?

or

Is there any counterexample?

Condition $$2$$ requires two groups are the same order type. If $$G$$ is a finite group and $$n\in \mathbb{N}$$, then $$G(n):=\{x\in G|x^{n}=1\}$$. We say that the groups $$G$$ and $$H$$ are of the same order type if $$|G(n)|=|H(n)|$$, for all $$n\in \mathbb{N}$$.

J. G. Thompson has a problem on the same order type group:

Let $$G$$ and $$H$$ be two groups of the same order type such that $$H$$ is solvable. Is $$G$$ solvable?

• You have changed the question, but it is still missing any context or motivation. – Derek Holt Apr 5 at 5:27
• @Derek Holt: Motivation of the question added. – M. T Apr 5 at 11:03
• So you are just re-asking Thompson's question? I guess I should vote to reopen then! – Derek Holt Apr 5 at 11:30


text:
# HiSET: Math : Cylinders

## Example Questions

### Example Question #1 : Use Volume Formulas To Solve Problems

What is the volume of a cylinder with a diameter of  cm and a height of  cm?

Explanation:

Step 1: Find the diameter.

If we are given the diameter, the length of the radius is one-half the diameter.


text:
Advent of Code 2021 - Problem 7
Dec 7, 2021
Luc Blassel

I am currently doing the advent of code 2021 programming challenge, which (at the time I’m writing this), is on day 7.

I got the motivation to write this post from this tweet that had some questions about the solution.

I am going to attempt to explain my approach to this problem and why we find this particular solution, so if you have not seen the problem I encourage it to try it yourself before reading this (have fun!).

# The first problem

## What’s the problem setting ?

You are in a submarine, deep under the ocean, when a giant whale decides to eat you. suddenly a bunch of crabs in tiny crab-submarines appear and decide to help you. To be able to help you the crabs need to align themselves, however, being crabs after all, they can only move sideways. The crab submarines have a limited amount of fuel, so you need to find the where the crabs should align in order to expend the smallest amount of fuel as possible. The puzzle input is the horizontal position of the crab.
In the given example there are n crabs at positions 16,1,2,0,4,2,7,1,2,14. We can represent this with a simple diagram, making a grid with 16 columns for all the possible horizontal crab position, a row per crab and marking the position of the crab with C:

  0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16
-------------------------------------------------
.  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  C
.  C  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .
.  .  C  .  .  .  .  .  .  .  .  .  .  .  .  .  .
C  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .
.  .  .  .  C  .  .  .  .  .  .  .  .  .  .  .  .
.  .  C  .  .  .  .  .  .  .  .  .  .  .  .  .  .
.  .  .  .  .  .  .  C  .  .  .  .  .  .  .  .  .
.  C  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .
.  .  C  .  .  .  .  .  .  .  .  .  .  .  .  .  .
.  .  .  .  .  .  .  .  .  .  .  .  .  .  C  .  .

Let’s say we want them to align at column 3, then our final crab positions will be:

  0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16
-------------------------------------------------
.  .  .  C  .  .  .  .  .  .  .  .  .  .  .  .  .
.  .  .  C  .  .  .  .  .  .  .  .  .  .  .  .  .
.  .  .  C  .  .  .  .  .  .  .  .  .  .  .  .  .
.  .  .  C  .  .  .  .  .  .  .  .  .  .  .  .  .
.  .  .  C  .  .  .  .  .  .  .  .  .  .  .  .  .
.  .  .  C  .  .  .  .  .  .  .  .  .  .  .  .  .
.  .  .  C  .  .  .  .  .  .  .  .  .  .  .  .  .
.  .  .  C  .  .  .  .  .  .  .  .  .  .  .  .  .
.  .  .  C  .  .  .  .  .  .  .  .  .  .  .  .  .
.  .  .  C  .  .  .  .  .  .  .  .  .  .  .  .  .

Our goal is to find the column in which to align them, for which the least amount of fuel will be consumed by the crabs. If we choose column $$3$$, then the first crab will have to spend $$16 - 3 = 13$$ units of fuel, the second crab will need $$3 - 1 = 2$$ units of fuel and so on.

## A brute force approach

This is very simple to solve with a brute force approach, we define a function to compute the cost of moving all the crabs to a column, apply this function to all possible columns and see which one is smallest:

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17  def compute_fuel_usage(crabs, destination): fuel_cost = 0 for crab in crabs: fuel_cost += abs(crab - destination) return fuel_cost crabs = [16, 1, 2, 0, 4, 2, 7, 1, 2, 14] min_fuel = -1 min_pos = 0 for destination in range(min(crabs), max(crabs) + 1): usage = compute_fuel_usage(crabs, destination) if usage < min_fuel or min_fuel < 0: min_fuel = usage min_pos = destination print(f"Crabs should move to position {min_pos}, using {min_fuel} fuel")

This will give us the (correct) answer of $$2$$ with a fuel cost of $$37$$. Now this is a fine solution for the test input but it will be very inefficient if we have more crabs and if they are more spread out.

## An analytical solution

The first thing I thought about is exploring significant points like the mean or the median of our crab positions. In our example above the mean is not the optimal solution however the median is equal to $$2$$, which is optimal. After a bit more saerching I found the geometric median, which is ” the point minimizing the sum of distances to the sample points” of a dataset. This is exactly what we are looking for, and per the wikipedia article, in a 1-dimensional setting (like ours) it is equal to the median. Bingo we have a very simple way of getting the optimal position: just take the median of our dataset, it is super quick and we only need to compute 1 thing. Our new code becomes:

 1 2 3 4 5 6  from statistics import median min_pos = median(crabs) min_fuel = compute_fuel_usage(min_pos) print(f"Crabs should move to position {min_pos}, using {min_fuel} fuel")

Through a bit of exploration I think anybody would have realized that the median is actually the optimum, however we can also derive it analytically and prove why the optimum is actually the median.
Our problem is in essence an optimization problem, we have a cost (the fuel usage) which depends on a parameter (the column in which to line up) and we want to minimize that cost w.r.t the chosen parameter. This is a very common framework and if the cost is a simple function we can derive an analytical solution to our problem.
First let’s define some terms:

• I will call $$n$$ the number of crabs
• $$x_i$$ is the horizonal position of the $$i^{th}$$ crab. So in our example above $$x_0=16$$ and $$x_1=1$$.
• $$\theta$$ is the x-position at which we want the crabs to align
• $$\theta^*$$ is the optimal value of $$\theta$$, so in our example above $$\theta^*=2$$
• $$C(\theta)$$ is the cost function (i.e the amount of fuel used) for a given value of $$\theta$$. In our example above $$C(2) = 37$$.

The first step in any optimization function is to define the cost function. In our case it’s quite simple, our cost is the sum of all the absolute differences between each crab and the chosen value of $$\theta$$: $$C(\theta) = \sum_{i=1}^n|x_i - \theta|$$

Now that we have this cost function how are we supposed to find the minimum you might ask ? If you have taken a calculus class this will no doubt sound familiar, we need to compute the derivative of $$C(\theta)$$ and find the value of $$\theta$$ for which it is equal to 0. That simple!
Now this cost function is simply a sum so it will be quite easy to compute its derivative. First we need to break it up, we can define the absolute value $$|x_i - \theta|$$ as follows:

$$|x_i - \theta| = \begin{cases} \theta - x_i &\text{if }x_i \leq \theta \\ x_i - \theta &\text{if }x_i > \theta\\ \end{cases}$$

So our cost function becomes:

\begin{align} C(\theta) &= \sum_{x_i \leq \theta} \big(\theta - x_i\big) + \sum_{x_i > \theta} \big(x_i - \theta\big) \\ &= \sum_{x_i \leq \theta} \theta - \sum_{x_i \leq \theta} x_i + \sum_{x_i > \theta} x_i - \sum_{x_i > \theta} \theta\\ \end{align}

If we take the derivative of this expression w.r.t $$\theta$$ both sums which only contain $$x_i$$ will be reduced to 0, and since the derivative of the sum is equal to the sum of the derivatives it is eay to compute the rest of the terms:

\begin{align} \frac{\partial\,C(\theta)}{\partial\theta} &= \frac{\partial}{\partial\theta}\bigg(\sum_{x_i \leq \theta} \theta - \sum_{x_i > \theta} \theta\bigg)\\ &= \sum_{x_i \leq \theta} \frac{\partial\,\theta}{\partial\theta} - \sum_{x_i > \theta} \frac{\partial\,\theta}{\partial\theta}\\ &= \sum_{x_i \leq \theta} 1 - \sum_{x_i > \theta} 1\\ \end{align}

There we have a simple definition of the derivative of our cost function w.r.t to the parameter we wish to optimize. Now to find $$\theta^*$$ we simply need to find where the derivative is equal to 0:

\begin{align} & \frac{\partial\,C(\theta^*)}{\partial\theta} = 0 \\ \Leftrightarrow & \sum_{x_i \leq \theta} 1 - \sum_{x_i > \theta} 1 = 0 \\ \Leftrightarrow & \sum_{x_i \leq \theta} 1 = \sum_{x_i > \theta} 1 \end{align}

You will notice that for our derivative to be equal to 0 we need to have as many points $$\leq\theta^*$$ as there are points $$>\theta^*$$, which is exaclty the definition of the median.
Take a minute to work through it by yourself and make sure I haven’t made any mistakes but by now it should make sense *why* the median is the optimal solution in our problem.

# The second problem

As is usual in advent of code problems, getting the correct answer in the first problem unlocks a second, harder, problem which builds upon the first. In our case the setting is the same except that we misunderstood the fuel usage of the crab submarines. Instead of using up 1 unit of fuel per unit of distance, they use up an additional unit of fuel for each unit of distance covered. For instance, a crab submarine that will travel 3 units of distance will use up $$1 + 2 + 3 = 6$$ units of fuel.

The brute force approach still works fine on the smaller test data, we simply need to update our compute_fuel_usage function:

 1 2 3 4 5 6  def compute_new_fuel_usage(crabs, destination): fuel_cost = 0 for crab in crabs: for i in range(1, abs(crab - destination) + 1): fuel_cost += i return fuel_cost

But once more this approach is super inneficient as we grow the number of crabs and the number of columns. So here it is better to consider this as an optimization problem once more. We simply need to redefine the cost function to fit our problem and we can follow the exact same steps as before to find $$\theta^*$$. And a way to write this cost is as follows:

$$C(\theta) = \sum_{i=1}^n\bigg( \sum_{j=1}^{|x_i - \theta|} j \bigg)$$

Where both sums corresponds to both loops of our compute_new_fuel_usage function. Now this cost function does not see, very derivative friendly so lets try to break it up. The first thing we need to know is that there is a forumla for the sum of the $$k$$ first natural integers:

$$\sum_{i=1}^{k} i = \frac{k \cdot (k + 1)}{2}$$

So in our case we can rewrite the cost function as:

\begin{align} C(\theta) &= \sum_{i=1}^n\bigg( \frac{|x_i - \theta| \cdot (|x_i - \theta| + 1)}{2} \bigg) \\ &= \sum_{i=1}^n\bigg( \frac{|x_i - \theta||x_i - \theta| + |x_i - \theta|}{2} \bigg) \\ &= \frac{1}{2}\sum_{i=1}^n\big((x_i - \theta)^2 + |x_i - \theta|\big) \\ &= \frac{1}{2}\bigg( \sum_{i=1}^n(x_i - \theta)^2 + \sum_{i=1}^n|x_i - \theta| \bigg) \\ &= \frac{1}{2}\bigg( \sum_{i=1}^n \big(x_i^2 - 2\cdot x_i\cdot\theta + \theta^2\big) + \sum_{i=1}^n|x_i - \theta| \bigg) \\ &= \frac{1}{2}\bigg(\sum_{i=1}^n x_i^2 - 2\sum_{i=1}^n x_i\cdot\theta + \sum_{i=1}^n \theta^2 + \sum_{x_i \leq \theta} \theta - \sum_{x_i \leq \theta} x_i + \sum_{x_i > \theta} x_i - \sum_{x_i > \theta} \theta\bigg) \end{align}

whoo that’s big and scary, but when we take the derivative w.r.t to $$\theta$$ all the sums that don’t depend on $$\theta$$ will disappear:

\begin{align} \frac{\partial\,C(\theta)}{\partial\theta} &= \frac{1}{2}\frac{\partial}{\partial\theta}\bigg( - 2\sum_{i=1}^n x_i\cdot\theta + \sum_{i=1}^n \theta^2 + \sum_{x_i \leq \theta} \theta - \sum_{x_i > \theta} \theta\bigg) \\ &= \frac{1}{2}\bigg( - 2\sum_{i=1}^n x_i + \sum_{i=1}^n 2\theta + \sum_{x_i \leq \theta}1 - \sum_{x_i > \theta}1 \bigg) \\ &= - \sum_{i=1}^n x_i + \sum_{i=1}^n\theta + \frac{1}{2}\bigg(\sum_{x_i \leq \theta}1 - \sum_{x_i > \theta}1\bigg) \end{align}

Let’s call the last term $$R$$ for notational simplicity and we have our derivative:

$$\frac{\partial C(\theta)}{\partial\theta} = - \sum_{i=1}^n x_i + \sum_{i=1}^n\theta + R$$

Now we just need to find the minimum:

\begin{align} & \frac{\partial C(\theta^*)}{\partial\theta} = 0\\ \Leftrightarrow &\; - \sum_{i=1}^n x_i + \sum_{i=1}^n\theta^* + R = 0 \\ \Leftrightarrow &\; \sum_{i=1}^n\theta^* = \sum_{i=1}^n x_i - R \\ \Leftrightarrow &\; n\cdot\theta^* = \sum_{i=1}^n x_i - R \\ \Leftrightarrow &\; n\cdot\theta^* = \sum_{i=1}^n x_i - R \\ \Leftrightarrow &\; \theta^* = \frac{1}{n}\sum_{i=1}^n x_i - \frac{R}{n} \\ \end{align}

Now we can assume that R divided by n is probably small if the dataset is well distributed 1. So our optimal value will be close to the mean of our crab positions:

$$\theta^* \approx \frac{1}{n}\sum_{i=1}^n x_i$$

And it is indeed a good place to start, so we can rewrite our code to look at the points around the mean to find the optimum:

  1 2 3 4 5 6 7 8 9 10 11 12  from statistics import mean m = mean(crabs) candidates = [m-1, m, m+1] min_pos, min_fuel = 0, -1 for candidate in candidates: fuel = compute_new_fuel_usage(positions, candidate) if fuel < min_fuel or min_fuel < 0: min_fuel = fuel min_pos = candidate print(f"Crabs should move to position {min_pos}, using {min_fuel} fuel")

This will allow us to find the optimal point much more efficiently!

# Parting words

I hope you understood the approach I took and if you are interested in my progress on advent of code 2021 you can check out my github repo for my python solutions (while I can solve the problems :p).
Thanks for reading and if you notice any mistakes in my reasonning please don’t hesitate to point them out to me!

1. N.B: as pointed out here the value of $$R$$ is actually bounded:
Since all $$x_i$$ and $$\theta$$ values are positive: $$0 \leq card({x_i\leq\theta}) \leq n$$ and $$0 \leq card({x_i>\theta}) \leq n$$. Therefore:

$$\begin{gather} -n \leq \sum_{x_o\leq\theta}1 - \sum_{x_o>\theta}1 \leq n \\ \Leftrightarrow \frac{-n}{2} \leq R \leq \frac{n}{2} \\ \Leftrightarrow \frac{-1}{2} \leq \frac{R}{n} \leq \frac{1}{2} \\ \end{gather}$$
This means that at most the optimum will be $$1/2$$ off of the mean, therefore the integer optimum must be at the integer mean $$\pm 1$$. ↩