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Could ketamine be the answer to treating treatment-resistant major depressive disorder?
2. Islam Ahmed Mansour
1. Psychiatry, Mansoura University Faculty of Medicine, Mansoura, Egypt
1. Correspondence to Dr Abdullah Mohammed Ramadan; boodi000{at}icloud.com

## Abstract

Major depressive disorder (MDD) is a common, serious, debilitating condition affecting 350 million people worldwide, which remains to be unsatisfactorily treated with 53% of patients still complaining of symptoms after completing their courses with the correct dosage. Ketamine, which was approved by the Food and Drug Administration in 2019, is a potential treatment option for those recalcitrant cases. The mechanism of ketamine is not fully understood, but as type it is classified as an N-methyl-D-aspartate (NMDA) glutamate receptor antagonist, and can be given intravenously, intranasally and orally. It is used to treat treatment-resistant depression, depression associated with suicidal ideation, mood and anxiety disorders and depressions associated with either type of bipolar disorder. Although ketamine is considered relatively safe, several side effects have been reported with the major ones being psychiatric in the form of worsening mood, anxiety and agitation; psychotomimetic in the form of dissociation, perceptual disturbance and abnormal sensations; cardiovascular in the form of increased blood pressure and increased heart rate; and neurological in the form of headache and dizziness. Ketamine is still not approved worldwide for usage in patients with treatment-resistant MDD, but if it is approved sometime in the future with relatively fewer side effects, it is expected to significantly save millions of dollars spent yearly on patients with treatment-resistant depression and that will lift this major burden off the shoulders of healthcare professionals. This study was designed to measure the effects of ketamine, an NMDA receptor antagonist, on patients with treatment-resistant MDD and to analyse the concept that makes it different and relatively safer than other major antidepressants like selective serotonin reuptake inhibitors, monoamine oxidase inhibitors and TCAs (tricyclic antidepressants).

• depressive disorder, treatment-resistant
• anxiety
• bipolar disorder
• depressive disorder, major

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## Introduction

Major depressive disorder (MDD) is a serious condition that affects the lives of many individuals globally. It is estimated that the total number of cases diagnosed with MDD is 350 million people around the world.1 2 And eight hundred thousand patients die every year due to suicidal ideation caused by MDD. MDD poses major burdens to the healthcare systems of different countries around the world.1–3 Despite the different treatment options available in the form of selective serotonin reuptake inhibitors (SSRI), tricyclic antidepressants (TCA) and monoamine oxidase inhibitors (MAOI), none of them were capable of completely relieving the symptoms of depression and many cases have reported frequent relapses, almost 53%, after completing the courses of their medications with the appropriate doses2 with 20% failing to show improvement on usage of subsequent lines of therapy.2 4 The current economic burden of MDD in the USA alone is estimated at $29–$48 billion per year.5 In fact, it carries a major economic burden in the form of the requirement of numerous emergency rooms, lacking of responsiveness to the current medications and major unemployment to many healthcare professionals.2 6

Currently, there is no consensus on the definition of treatment-resistant depression (TRD), but the current definition is that it is any form of depression in which the patient is not fully relieved from the major symptoms of depression after taking the appropriate courses of at least two antidepressant medications at their adequate time duration.2–5 The main limitation in the usage of these agents, besides the lack of appropriate responsiveness, is the fact that they could take more than 2–4 weeks in order for the initial response to be felt by the patients; in addition numerous studies have shown that many patients report multisystemic, unbearable side effects.7 8

In March 2019, the US Food and Drug Administration (FDA) approved a new antidepressant medication under the name of ketamine, an N-methyl-D-aspartate (NMDA) type of glutamate receptor antagonist. This review is dedicated to knowing the pharmacological details of this medication and how it is different from other antidepressants in the management of TRD.7 8

Ketamine is not a perfect drug. Although studies in many patients have been shown to produce positive results in patients with TRD, they have shown that significant side effects have caused many cases to cease undergoing drug trials. Especially patients with chronic cardiovascular conditions like myocardial infarction, arteriovenous fistulae and chronic hypertension should not be allowed to use ketamine.

## Uses and dosage

Ketamine is an NMDA receptor antagonist that is used in the management of TRDs, depression associated with suicidal ideation, mood and anxiety disorders and depressions associated with either type of bipolar disorder. Unlike other NMDA antagonists, like memantine that is used in the symptomatic management of Alzheimer’s disease, the mechanism by which ketamine deals with depression follows a different pathway. It is not fully understood how ketamine treats depression, but it works by different mechanisms. Ketamine could be given by three different methods: orally, intravenously and nasally.9 10

### Intravenously

The majority of the randomised controlled trials using a dose of 0.5 mg/kg over 40 min of intravenous ketamine followed by a 20% saline infusion washout have shown significant improvement in depression symptoms and suicidal ideation within 1 week as measured using the Montgomery and Asberg Depression Rating Scale (MADRS).11 12 Response rates for patients using intravenous ketamine were shown to be 50%–70%, which proves to be better than other classes of antidepressants.13 14 Most of the patients have not reported any serious side effects12; however, some patients decided to stop taking the drug after showing major side effects.

### Intranasal

The US FDA has recently approved the usage of intranasal esketamine along with an oral antidepressant. The doses used in most of the studies were an initial dose of 28 mg/kg and a maintenance dose of 56 or 84 mg/kg. Most cases have statistically shown significant improvements over 40 min according to the MADRS score. Some major side effects were shown in some patients mainly because of the high level of bioavailability of esketamine as it has no first-pass metabolism.15

Those side effects included dissociation, fatigue, poor memory, severe headaches, nausea, elevated heart rate and blood pressure.

### Oral

Oral ketamine undergoes a high level of the first-pass metabolism which makes its bioavailability less than 20%. A small open-label study of oral ketamine with a dose of 0.5 mg/kg in hospice patients for 28 days has shown a significant improvement in the MADRS depression scale.16–18 The time to response was 1–2 weeks; however, some patients have decided to withdraw from the trial due to lack of response. Dizziness, delirium, hallucinations, nausea, vomiting and headache were the reported side effects in most of the studies.9

## Mechanism of action

Currently, there is no full consensus among authors on the exact mechanism/s by which ketamine plays a role in the management of TRD. Basically, ketamine is an antagonist that blocks the NMDA receptors, but evidence based on numerous studies has proven that the rapid antidepressant (RAAD) effect that ketamine establishes is not based on its NMDA receptor antagonism. While other FDA-approved antidepressants have their antidepressant roles derived from their effects on monoamines such as serotonin, norepinephrine and dopamine, the emergence of ketamine has provided a new perspective that is based on its effects on the glutamate system providing RAAD effects within 4 hours with a long-term effect that lasts for 1 week after a single dose.19

Numerous publications have stated that ketamine induces synaptogenesis at the level of the prefrontal cortex, a part of the brain that atrophies in depressed patients.20 Other studies have also shown that ketamine upregulates the activity of a certain type of receptors called glutamate alpha-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) which plays an important role in increasing the levels of the mammalian target of rapamycin (mTOR) which induces synaptogenesis at the level of the prefrontal cortex.21 22 Some authors have come to merge the two hypotheses, as shown in figure 1, concluding that the NMDA receptor antagonistic effect of ketamine on GABAergic interneurons induces the release of glutamate from the prefrontal cortex which in turn activates the AMPA receptors. This activation has been shown to urge the release of brain-derived neurotrophic factor and vascular endothelial growth factor, both of which act on inducing the mTOR, which induces synaptogenesis at the prefrontal cortex level.23–25 This cycle is thought to be relevant to the antidepressant effect of ketamine.

Figure 1

Ketamine works by two currently merged mechanisms: N-methyl-D-aspartate (NMDA) receptor and alpha-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) receptor mechanisms. The NMDA receptor antagonistic effect of ketamine on GABAergic interneurons induces the release of glutamate from the prefrontal cortex which in turn activates the AMPA receptors. AMPAR, AMPA receptor; BDNF, brain-derived neurotrophic factor; GABA, gamma-aminobutyric acid; GLT-1, glutamate transporter 1; NMDAR, NMDA receptor.

## Side effects

Side effects reported from 60 studies have shown a variety of adverse effects affecting various body systems: psychiatric, cardiovascular, neurological, cognitive and others. Those studies involved 899 patients who received at least one dose of ketamine.26 Psychiatric side effects were described in 38% of the studies, whereas psychotomimetic ones were described in 72%. The psychiatric side effects included most commonly anxiety, followed by agitation and irritability, delusions and mood elevation. Less common side effects included detachment, emotional blunting, psychosis, craving attention and formal thought disorder. Only one case of suicidal attempt was reported in one study.27 The most commonly reported side effects from most studies that led the participants to withdraw from the trial included worsening mood (12 participants), anxiety (6 participants) and suicidal ideation (5 participants). The psychotomimetic side effects most commonly included dissociation, perceptual disturbance, odd or abnormal sensation, derealisation, hallucinations and depersonalisation. The only cases reported to withdraw from the trials were the ones who suffered dissociation.28 29 Most studies that used the intravenous route of administration rather than the other routes were the ones who mostly had psychiatry and psychotomimetic side effects. WHO has classified ketamine as a Schedule III drug as it carries a potential risk for addiction and abuse. It can be abused in any administered form, intravenously, orally or nasally. Ketamine has a potential risk of abuse by patients self-medicating themselves from depression.

Thirty-eight percent of the 60 studies reported cardiovascular side effects. Most of these changes were in the form of increased blood pressure, increased heart rate, arrhythmia, palpitations, dizziness, chest tightness and decreased blood pressure on standing. Only five cases withdrew from the studies due to serious cardiovascular effects. Most of those effects were also reported on the usage of intravenous ketamine infusion. Those effects only lasted 90 min reportedly.

The most commonly reported neurological side effects were headache and dizziness. The most commonly reported cognitive side effects included poor memory, poor concentration, confusion and cognitive impairment.

Multiple other side effects were reported in 32 (53%) of the studies, these side effects were mainly gastrointestinal, ocular, respiratory and urological.

The most frequently reported other side effects included blurred vision and nausea. Less commonly reported ones were insomnia, general malaise, fatigue, restlessness, dry mouth, vomiting and tearfulness.27

## Drug–drug interactions

Certain types of drugs should not be used concomitantly with any form of ketamine. Some of these drugs can interfere with the first-pass metabolism in case of being used with oral or intravenous ketamine, others may cause cardiovascular problems especially in individuals with cardiovascular diseases. Such drugs include benzodiazepines, antipsychotics, opioids and alcohol which may all cause sedation. Blood pressure and heart monitoring should be measured in case of using drugs like MAOIs, TCAs, SSRIs, modafinil, armodafinil and amphetamine types of drugs.30 Clonidine can be used safely with esketamine as it can reduce esketamine’s ability to cause hypertension and other side effects.31 Midazolam reduces the sympathomimetic effects of ketamine.32 Certain CYP(Cytochrome P450) enzyme inducers like rifampicin can reduce the concentration of esketamine and norketamine by 10% and 50%, respectively.33 Coadministration of ketamine and ticlopidine has been proven to increase the maximum plasma concentration of ketamine by 72% and total hepatic clearance by 15.5%.34

## Conclusions

Since getting approved for usage by the FDA in March 2019, ketamine has been a glimpse of hope to patients with treatment-resistant MDD due to its rapid efficacy and relatively less adverse effects in comparison to other antidepressant medications. This has proved some relief to the patients, their families, clinicians and world governments’ healthcare budgets as well as to the economic burden that treating patients with depression causes to healthcare institutes. However, this interest should not become absolute as the studies that were made for testing ketamine are relatively small and some of the studies made showed considerable risks for abuse and addiction. In addition, ketamine had been shown to cause many side effects in multiple cases. Further studies should be made focused on understanding more about the mechanism of action of ketamine, as most of the studies differ quite significantly on how ketamine acts on depression. They should also focus on limiting the potential risk of addiction that ketamine carries. That could further help in increasing the efficacy and limiting the adverse effects of ketamine.

## References

Abdullah Mohammed Hassan Ramadan is a 6th year Medical Student in Mansoura Manchester Program for Medical Education, University of Mansoura in Egypt. His main research interests include neurotransmitter receptors and their functions in drugs with different mechanisms of action, and medications for depression.

## Footnotes

• Contributors Both authors only have contributed to the work published.

• Funding The authors have not declared a specific grant for this research from any funding agency in the public, commercial or not-for-profit sectors.

• Competing interests None declared.

• Patient consent for publication Not required.

• Provenance and peer review Not commissioned; externally peer reviewed.

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Now you are in the subtree of Lecture Notes public knowledge tree.

Теория вероятностей

##test $\delta$ $\mathcal{B}$


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Definitions

# Jerk

[jurk]
In physics, jerk, jolt (especially in British English), surge or lurch, is the rate of change of acceleration; that is, the derivative of acceleration with respect to time, the second derivative of velocity, or the third derivative of displacement. Jerk is defined by the following equation:
$vec j=frac \left\{mathrm\left\{d\right\} vec a\right\} \left\{mathrm\left\{d\right\}t\right\}=frac \left\{mathrm\left\{d\right\}^2 vec v\right\} \left\{mathrm\left\{d\right\}t^2\right\}=frac \left\{mathrm\left\{d\right\}^3 vec r\right\} \left\{mathrm\left\{d\right\}t^3\right\}$
where
$vec a$ is acceleration,
$vec v$ is velocity,
$vec r$ is displacement
$mathit\left\{t\right\}$ is time.

Jerk is a vector, and there is no generally used term to describe its scalar magnitude.

The units of jerk are metres per second cubed (Metres per second per second per second, m/s3 or ms-3). There is no universal agreement on the symbol for jerk, but j is commonly used.

## Related concepts

Yank is sometimes used as the analog of force with respect to jerk: mass times jerk, or equivalently, the derivative of force with respect to time.

Higher derivatives of displacement are rarely necessary, and hence lack agreed-on names. The fourth derivative of position was considered in development of the Hubble Space Telescope's pointing control system, and called jounce. Many other suggestions have been made, such as jilt, jouse, jolt, and delta jerk. As more distinct terms that start with letters other than "j", the term snap has been proposed for the 4th derivative of position, with "crackle" and "pop" having been suggested – facetiously – as names for the 5th and 6th derivatives.


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## Limit of normalized quadrangulations: the Brownian map.(English)Zbl 1117.60038

The authors built the so-called Brownian map or “continuum random map”, as $$n\to\infty$$ of suitably scaled (with scaling $$n^{1/4}$$) random quadrangulations chosen equally likely among the pointed quadrangulations with $$n$$ faces. A metric space of pointed abstract maps containing the discrete pointed quadrangulations is constructed and the convergence is weak in this space, the limit being continuous and compact. This limit is described with the help of the Brownian snake with lifetime process the normalized Brownian excursion. First, the authors study a model of rooted quadrangulations which converges to the Brownian map. A model of rooted quadrangulations with random edge lengths is also shown to converge to the Brownian map. By using the canonical surjection from the set of rooted quadrangulations with $$n$$ faces onto the set of pointed quadrangulations with $$n$$ faces one obtains the first announced result. The convergence of the radius and of the profile of rooted and pointed quadrangulations are also studied.

### MSC:

 60F99 Limit theorems in probability theory 60K35 Interacting random processes; statistical mechanics type models; percolation theory 60C05 Combinatorial probability 60F05 Central limit and other weak theorems
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### References:

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# Thread: Help getting started on a problem (intro linear algebra)

1. ## Help getting started on a problem (intro linear algebra)

Q: Suppose $\displaystyle A=\begin{bmatrix}a&b\\c&d&\end{bmatrix}$. Find conditions on $\displaystyle a,b,c,$and $\displaystyle d$ for which $\displaystyle A^{-1}=A$. Then find two different matrices, other than the identity matrix, for which $\displaystyle A^{-1}=A$.

Do I just set up an equation to find what $\displaystyle A^{-1}$ is and then equate that to $\displaystyle A$ to find out when $\displaystyle A^{-1}=A$?

Or could I use the face that if $\displaystyle A^{-1}=A \Rightarrow A^{2}=I$?

Im not really sure to I pull everything together.

Thanks

2. You are correct. If $\displaystyle A=A^{-1}$, then $\displaystyle A^{2}=I$

$\displaystyle \begin{bmatrix}a&b\\c&d\end{bmatrix}$$\displaystyle \cdot \begin{bmatrix}a&b\\c&d\end{bmatrix}=\begin{bmatri x}1&0\\0&1\end{bmatrix}$

$\displaystyle \begin{bmatrix}a^{2}+bc&ab+bd\\ac+cd&bc+d^{2}\end{ bmatrix}=\begin{bmatrix}1&0\\0&1\end{bmatrix}$

$\displaystyle a^{2}+bc=1$
$\displaystyle ab+bd=0$
$\displaystyle ac+cd=0$
$\displaystyle bc+d^{2}=1$

One such matrix that fits is $\displaystyle \begin{bmatrix}1&0\\-3&-1\end{bmatrix}$


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# Trick LaTeX into doing double superscripts

I have a function in my .sty sheet that does a second partial derivative:

\newcommand{\hpartdsq}[2]{\dfrac{\partial^2 #1}{\partial #2 ^2}}

But I'd like to pass it something that already has a superscript (today it's \rho^*).

Is there a way to do this with this function? I feel like wrapping the \rho^* with parentheses would really kill the aesthetics and is not typical for second partial derivatives. Thanks!

-

One cheap solution is to call the macro like this: \hpartdsq{f}{{\rho^*}}.

EDIT: Maybe I should add that it's not a good idea to modify the macro definition so that it contains the braces {}: If you call this macro

\newcommand{\hpartdsq}[2]{\dfrac{\partial^2 #1}{\partial{#2}^2}}

with \hpartdsq{f}{\rho^*}, then it looks as desired, but with \hpartdsq{f}{x_1} the ^2 will be too far to the right.

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Wow! No wonder google couldn't help me! This is the perfect solution. Thanks! –  Richard Herron Nov 24 '10 at 17:07
@ricardh A good rule of thumb when you are having issues with latex not parsing your intended grouping correctly is to stuff it in brackets. Its the latex equivalent of putting parenthesis around mathematical expressions to explicitly state the order of operations. –  crasic Nov 26 '10 at 8:29
Thanks, I wasn't planning on altering the orig function with this, just applying it as needed. –  Richard Herron Nov 27 '10 at 4:35


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Issue No.03 - March (2006 vol.17)
pp: 227-240
ABSTRACT

Abstract—A <it>many-to-many k-disjoint path cover</it> (k-DPC) of a graph <tmath>G</tmath> is a set of <tmath>k</tmath> disjoint paths joining <tmath>k</tmath> distinct source-sink pairs in which each vertex of <tmath>G</tmath> is covered by a path. We deal with the graph <tmath>G_0 \oplus G_1</tmath> obtained from connecting two graphs <tmath>G_0</tmath> and <tmath>G_1</tmath> with <tmath>n</tmath> vertices each by <tmath>n</tmath> pairwise nonadjacent edges joining vertices in <tmath>G_0</tmath> and vertices in <tmath>G_1</tmath>. Many interconnection networks such as hypercube-like interconnection networks can be represented in the form of <tmath>G_0 \oplus G_1</tmath> connecting two lower dimensional networks <tmath>G_0</tmath> and <tmath>G_1</tmath>. In the presence of faulty vertices and/or edges, we investigate many-to-many disjoint path coverability of <tmath>G_0 \oplus G_1</tmath> and <tmath>(G_0 \oplus G_1) \oplus (G_2 \oplus G_3)</tmath>, provided some conditions on the Hamiltonicity and disjoint path coverability of each graph <tmath>G_i</tmath> are satisfied, <tmath>0 \leq i \leq 3</tmath>. We apply our main results to recursive circulant <tmath>G(2^m,4)</tmath> and a subclass of hypercube-like interconnection networks, called <it>restricted HL-graphs</it>. The subclass includes twisted cubes, crossed cubes, multiply twisted cubes, Möbius cubes, Mcubes, and generalized twisted cubes. We show that all these networks of degree <tmath>m</tmath> with <tmath>f</tmath> or less faulty elements have a many-to-many <tmath>k{\hbox{-}}{\rm{DPC}}</tmath> joining any <tmath>k</tmath> distinct source-sink pairs for any <tmath>k \geq 1</tmath> and <tmath>f \geq 0</tmath> such that <tmath>f+2k\leq m-1</tmath>.

INDEX TERMS
Fault tolerance, network topology, graph theory, fault-Hamiltonicity, embedding, strong Hamiltonicity, recursive circulants, restricted HL-graphs.
CITATION
Jung-Heum Park, Hee-Chul Kim, Hyeong-Seok Lim, "Many-to-Many Disjoint Path Covers in Hypercube-Like Interconnection Networks with Faulty Elements", IEEE Transactions on Parallel & Distributed Systems, vol.17, no. 3, pp. 227-240, March 2006, doi:10.1109/TPDS.2006.37


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# 计算机代写|计算机网络代写computer networking代考|CS402

## 计算机代写|计算机网络代写computer networking代考|Client and Server Processes

A network application consists of pairs of processes that send messages to each other over a network. For example, in the Web application a client browser process exchanges messages with a Web server process. In a P2P file-sharing system, a file is transferred from a process in one peer to a process in another peer. For each pair of communicating processes, we typically label one of the two processes as the client and the other process as the server. With the Web, a browser is a client process and a Web server is a server process. With P2P file sharing, the peer that is downloading the file is labeled as the client, and the peer that is uploading the file is labeled as the server.

You may have observed that in some applications, such as in P2P file sharing, a process can be both a client and a server. Indeed, a process in a P2P file-sharing system can both upload and download files. Nevertheless, in the context of any given communication session between a pair of processes, we can still label one process as the client and the other process as the server. We define the client and server processes as follows:

In the context of a communication session between a pair of processes, the process that initiates the communication (that is, initially contacts the other process at the beginning of the session) is labeled as the client. The process that waits to be contacted to begin the session is the server.

In the Web, a browser process initializes contact with a Web server process; hence the browser process is the client and the Web server process is the server. In P2P file sharing, when Peer A asks Peer B to send a specific file, Peer A is the client and Peer B is the server in the context of this specific communication session. When there’s no confusion, we’ll sometimes also use the terminology “client side and server side of an application.” At the end of this chapter, we’ll step through simple code for both the client and server sides of network applications.

## 计算机代写|计算机网络代写computer networking代考|The Interface Between the Process and the Computer Network

As noted above, most applications consist of pairs of communicating processes, with the two processes in each pair sending messages to each other. Any message sent from one process to another must go through the underlying network. A process sends messages into, and receives messages from, the network through a software interface called a socket. Let’s consider an analogy to help us understand processes and sockets. A process is analogous to a house and its socket is analogous to its door. When a process wants to send a message to another process on another host, it shoves the message out its door (socket). This sending process assumes that there is a transportation infrastructure on the other side of its door that will transport the message to the door of the destination process. Once the message arrives at the destination host, the message passes through the receiving process’s door (socket), and the receiving process then acts on the message.

Figure $2.3$ illustrates socket communication between two processes that communicate over the Internet. (Figure $2.3$ assumes that the underlying transport protocol used by the processes is the Internet’s TCP protocol.) As shown in this figure, a socket is the interface between the application layer and the transport layer within a host. It is also referred to as the Application Programming Interface (API) between the application and the network, since the socket is the programming interface with which network applications are built. The application developer has control of everything on the application-layer side of the socket but has little control of the transport-layer side of the socket. The only control that the application developer has on the transportlayer side is (1) the choice of transport protocol and (2) perhaps the ability to fix a few transport-layer parameters such as maximum buffer and maximum segment sizes (to be covered in Chapter 3). Once the application developer chooses a transport protocol (if a choice is available), the application is built using the transport-layer services provided by that protocol. We’ll explore sockets in some detail in Section $2.7$.

# 计算机网络代考

. conf

. conf

## 计算机代写|计算机网络代写computer networking代考|The Interface Between the Process and the Computer Network

myassignments-help数学代考价格说明

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Math作业代写、数学代写常见问题

myassignments-help擅长领域包含但不是全部:


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## S 4 years ago An object is thrown up from a height of 160 feet. Its velocity at t is v(t)=-32t+24 ft/ sec a) how high will it go? b) with what velocity will it hit the ground?

1. anonymous

max height is at the vertex. use $$t=-\frac{b}{2a}$$ to find it

2. anonymous

oh but first you need the equation. it is $h(t)=-16t^2+v_0t+h_0$ in your case $$h_0=160$$ and $$v_0=$$ hmm confused. what is the initial velocity?

3. anonymous

oh it is 24, so your equation is $h(t)=-16t^2+24t+160$ max when $$t=\frac{24}{32}=\frac{3}{4}$$ replace $$t$$ by $$\frac{3}{4}$$ to find the max height

4. anonymous

thank you


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# High Performance GHASH Function for Long Messages

2 DALI - Digits, Architectures et Logiciels Informatiques
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier, UPVD - Université de Perpignan Via Domitia
Abstract : This work presents a new method to compute the GHASH function involved in the Galois/Counter Mode of operation for block ciphers. If $X= X_1\dots X_n$ is a bit string made of $n$ blocks of 128 bits each, then the GHASH function effectively computes $X_1H^n + X_2H^{n-1} + \dots X_nH$, where $H$ is an element of the binary field $\Fd_{2^{128}}$. This operation is usually computed by using $n$ successive multiply-add operations over $\Fd_{2^{128}}$. In this work, we propose a method to replace all but a fixed number of those multiplications by additions on the field. This is achieved by using the characteristic polynomial of $H$. We present both how to use this polynomial to speed up the GHASH function and how to efficiently compute it for each session that uses a new $H$.
Document type :
Conference papers

Cited literature [15 references]

https://hal.archives-ouvertes.fr/hal-01279437
Contributor : Nicolas Méloni <>
Submitted on : Friday, February 26, 2016 - 11:26:43 AM
Last modification on : Tuesday, June 19, 2018 - 3:50:01 PM
Long-term archiving on: : Friday, May 27, 2016 - 10:20:56 AM

### File

HighPerfGHASH.pdf
Files produced by the author(s)

### Citation

Nicolas Méloni, Christophe Negre, M. Anwar Hasan. High Performance GHASH Function for Long Messages. ACNS: Applied Cryptography and Network Security, 2010, Beijing, China. pp.154-167, ⟨10.1007/978-3-642-13708-2_10⟩. ⟨hal-01279437⟩

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# Ranked voting system

(Redirected from Ranked voting systems)

Preferential voting or rank voting describes certain voting systems in which voters rank outcomes in a hierarchy on the ordinal scale. When choosing between more than two options, preferential voting systems provide a number of advantages over first-past-the-post voting (also called plurality voting). This does not mean that preferential voting is always the best system; Arrow's impossibility theorem proves that no method can simultaneously obtain all properties desirable in a voting system.[Mankiw 1] There is likewise no consensus among academics or public servants as to the best electoral system.[1]

There are many types of preferential voting, but currently only instant-runoff voting (alternative vote) and single transferable vote are used in governmental elections. Instant runoff voting is employed in Australia at the state and federal levels, in Ireland for its presidential elections, and by some cities in the United States, United Kingdom, and New Zealand. The single transferable vote is used for national elections in the Republic of Ireland and Malta, for regional and local elections in Northern Ireland, for all local elections in Scotland, and for some local elections in New Zealand and the United States.

## Variety of systems

There are many preferential voting systems, so it is sometimes difficult to distinguish between them.

Selection of the Condorcet winner is generally considered by psephologists as the ideal election outcome,[2] so "Condorcet efficiency" is important when evaluating different methods of preferential voting.[3] This choice is also the one that would win every two-way contest against every other alternative.[Mankiw 2]

Another criterion used to gauge the effectiveness of a preferential voting system is its ability to withstand manipulative voting strategies,[4] when voters cast ballots that do not reflect their preferences in the hope of electing their first choice. This can be rated on at least two dimensions—the number of voters needed to game the system[5] and the complexity of the mechanism necessary.[citation needed]

### Instant-runoff or preferential voting

Used in national elections in Australia, this system simulates a series of runoff elections. If no candidate is the first choice of more than half of the voters, then all votes cast for the candidate with the fewest number of first choices are added to the totals of the top-ranked candidate still in the race.[6] If this does not result in any candidate receiving a majority, further rounds of redistribution occur.[6]

This method is thought to be resistant to manipulative voting as the only strategies that work against it require voters to highly rank choices they actually want to see lose.[G&F 1] At the same time, this system fails the monotonicity criterion, where ranking a candidate higher can lessen the chances he or she will be elected. Additionally, alternative voting has a lower Condorcet efficiency than similar systems when there are more than four choices.[G&F 2]

### Borda count

In the Borda count, ballots are counted by assigning a point value to each place in each voter's ranking of the candidates, and the choice with the largest number of points overall is elected.[Mankiw 1] This method is named after its inventor, French mathematician Jean-Charles de Borda.[Mankiw 1] Instead of selecting a Condorcet winner, this system may select a choice that reflects an average of the preferences of the constituency.[citation needed]

However, as explained in the main article, in some circumstances the Borda count may degenerate into a first-past-the-post ballot.

This system suffers from the fact that the outcome it selects is dependent on the other choices present[clarification needed]. That is, the Borda count does not exhibit independence of irrelevant alternatives[Mankiw 1] or independence of clones. The implication here is that a Borda count can be easily manipulated simply by including additional candidates.[citation needed]

### Single transferable vote

This is currently one of the preferential voting systems most used by countries and states.[notes 1] It uses multi-member constituencies. Any candidates that achieve the number of votes required for election (the "quota") are elected and their surplus votes are redistributed to the voter's next choice candidate.[CEPPS 1] Once this is done, if not all places have been filled then the candidate with the smallest amount of votes is eliminated, and their votes are also redistributed to the voter's next choice. This whole process is repeated until all seats are filled. This method is also called the Hare-Clark system.[CEPPS 1]

1. ^ See table in use by polities below

## Superiority v. FPTP

When choosing between more than two options, preferential voting achieves outcomes better than those produced by a first-past-the-post system. When endorsing a switch to a preferential voting system in 2011, British politician Nick Clegg stated, "first-past-the-post leads to a whole host of problems... it means MPs can go about their business without ever having to appeal to a majority of their own constituents...".[8] He also stated that a preferential voting method like instant runoff voting would result in politicians "work[ing] harder to appeal to more people than before".[8] Academic experts have also rejected first-past-the-post; at a 2011 LSE workshop attended by 22 voting theory specialists, none endorsed first-past-the-post as the "best voting procedure".[9]

The first-past-the-post system will indeed occasionally elect a candidate who would have lost out to every other option in a two-way contest (the so-called Condorcet loser) by splitting the opposition vote. It happens even more frequently (for a similar reason) that the winner is not the Condorcet winner.[Mankiw 2]

Many countries use a two-round system (a runoff election) to improve the fairness of the election.

Many arguments for preferential voting being superior to first-past-the-post rely to some extent on several assumptions: that voters have single peaked preferences over a single dimension (e.g. liberal v. conservative), that choices can be placed on a continuum, and that voters know accurately where each candidate lies on that continuum. However even if these assumptions are only partially true, the first-past-the-post system is still likely to be less fair.

If there are a large number of candidates, which is quite common in Single transferable vote elections, then it is likely that many preference voting patterns will be unique to individual voters.[10][11] For example, in the Irish general election, 2002, the electronic votes were published for the Dublin North constituency.[12] There were 12 candidates and almost 44,000 votes cast. The most common pattern (for the three candidates from one party in a particular order) was chosen by only 800 voters, and more than 16,000 patterns were chosen by just one voter each.

The number of possible complete rankings with no ties is the factorial of the number of candidates, N, but with ties it is equal to the corresponding ordered Bell number and is asymptotic to

$\frac{N!}{2(\ln 2)^{N+1}}$.[13]

In the case common to IRV in which no ties are allowed, except for unranked candidates who are tied for last place, the number of possible rankings for N candidates is precisely

$\sum_{n=1}^{N-1} \frac{N!}{n!} = \lfloor (e-1)N! - 1 \rfloor = \mathrm{floor}\left( (e-1)N! - 1 \right)$.[14]

## Use by polities

Countries
 Nation Year of first use Type Notes Australia 1918[15] single transferable vote, alternative vote From 1949, the single transferable vote method has been used for upper house legislative elections.[Sawer 1] Alternative vote is used for lower house elections.[CEPPS 2] Austria 1949[16] open list[1] Belgium 1945[16] open list[1] Brazil x open list[17] Chile[17] 1958-1973 open list Colombia[CEPPS 3] x open list Political parties choose between open list and closed list Cyprus x open list[1] Czech Republic[CEPPS 4] x contingent vote only used to decide lower house legislative elections Denmark 1945[16] open list[1] Estonia x open list[CEPPS 5] As of 2001 single transferable vote had been in use since 1990 to decide legislative elections.[Sawer 1] This is no longer the case.[CEPPS 5] Estonia's current open list system may not actually be a preferential voting system as it may be that voters cast only one preference vote. Fiji[18] 1998 alternative vote Finland 1945[16] open list[1] Greece 1975-1984, 1996[16] open list[1] Hong Kong 1998[19] alternative vote[20] alternative vote is only used in the 4 smallest of Hong Kong's 29 functional constituencies.[21] Officially called preferential elimination voting, the system is identical to the alternative vote.[20] Indonesia 2004[22] open list only used to decided the elections of one legislative chamber[CEPPS 6] Iraq[23] 2009 open list Ireland[Sawer 1] 1922 alternative vote, single transferable vote Single transferable vote is used to decide legislative elections only.[Sawer 1] Since 1937 Ireland has used the alternative vote to decide presidential elections.[Sawer 1] Italy 1946-1994[16] open list[24] Latvia[CEPPS 7] x open list only used to decide legislative elections Liechtenstein x open list[1] Luxembourg 1945[16] open list[CEPPS 8] Malta[Sawer 1] 1921 single transferable vote Nauru 1968[Sawer 1] Borda count[CEPPS 9] Nauru uses the Dowdall system, which is an improved version of the Borda count.[CEPPS 9] Netherlands 1945[16] open list[CEPPS 10] only used to decide lower house legislative elections[CEPPS 10] New Zealand x single transferable vote[25] alternative vote is used in only some elections, such as district health boards as well as some city and district councils.[25] Northern Ireland 1973[Sawer 1] single transferable vote[26] Norway 1945[16] open list[CEPPS 11] Papua New Guinea 2007[27] alternative vote[G&F 3] Between 1964 and 1975 PNG used a system that allowed voters the option of ranking candidates.[Sawer 1] Currently, voters must rank only their top three choices.[28] San Marino x open list[1] Slovakia[CEPPS 12] x open list only used to decide legislative elections Slovenia 2000[29] open list[CEPPS 13] Open list is only used to decide lower house legislative elections, and two seats, which are reserved for Hungarian and Italian minorities, are decided using a Borda count.[CEPPS 13] Sri Lanka[Sawer 2] 1978 contingent vote and open list[CEPPS 14] In Sri Lanka contingent vote is used to decide presidential elections[Sawer 1] and legislative elections, open list.[CEPPS 14] Switzerland x open list[17] Zimbabwe[30] 1979-1985 alternative vote only used for white candidates
Federated states
 Province/state Country Years in use Type Notes Alberta[Sawer 1] Canada 1952-1954 open list Australian Capital Territory[Sawer 1] Australia 1993–present single transferable vote British Columbia[Sawer 1] Canada 1926-1955 open list Manitoba[Sawer 1] Canada 1927-1936 open list New South Wales[Sawer 1] Australia 1918–present single transferable vote (1918-1926), contingent vote (1926-1928), alternative vote (1929-1980), open list (1981–present) Since 1978, NSW has used the single transferable vote method to decide upper house legislative elections only. Northern Territory[Sawer 1] Australia 1980 only[citation needed] x Queensland[Sawer 1] Australia 1892-1942, 1962–present contingent vote (1892-1942), alternative vote (1962-1992), open list (1992–present) South Australia[Sawer 1] Australia 1929-1935, 1982–present Alternative vote in multi-member districts (1929-1935), single transferable vote (1982–present) used to decide upper house legislative elections only Tasmania[Sawer 1] Australia 1907–present single transferable vote Since 1909, alternative vote voting has been used in Tasmania to decide upper house legislative elections. Victoria[Sawer 1] Australia 1911–present open list (1911-1915), alternative vote (1916–present) Prior to 1916, Victoria did not use any preferential voting method to decide upper house legislative elections. Western Australia[Sawer 1] Australia 1907–present open list (1907-1911), alternative vote (1912–present) Since 1989, Western Australia has used the single transferable vote method to decide upper house legislative elections
International organizations
 Organization Year of first use Type Notes European Union[CEPPS 15] x option to use single transferable vote Member countries can use either proportional representation (not a type of preferential voting)[citation needed] or single transferable vote to elect MEPs
Municipalities
 City/town Years in use Type Notes Ann Arbor, MI[31] 1975 only alternative vote Aspen, CO[32] 2009 only alternative vote Berkeley, CA[33] 2010–present alternative vote Burlington, VT[34] 2005-2010 alternative vote Hendersonville, NC[35] 2007–present alternative vote part of a statewide pilot program[36] London 2000[37]-present supplementary vote[38] Memphis, TN[6] 2011–present alternative vote Minneapolis, MN[39] 2009–present alternative vote Oakland, CA[33] 2010–present alternative vote Portland, ME[6] 2011–present alternative vote San Francisco 2004[40]-present alternative vote[6] San Leandro, CA[33] 2010–present alternative vote St. Paul, MN 2011[41]-present alternative vote[42] Takoma Park, MD[43] 2006–present alternative vote Telluride, CO[44] 2011–present alternative vote


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Robert Braeunig's excellent Rocket and Space Technology which provided most of the math powering these calculations. Physics is divided into specific, generic subjects from; the scientific constants, through atoms and orbits to the 'Big-Bang'. The table cells that are shaded blue are links to the KSP Forums, to indicate open source tools and compatibility with the latest version of KSP. Moon at perigee and apogee: 2001 to 2100. So, you want to calculate orbits? The lunar orbital radius R is a function of total energy, however the total orbital energy comes form two sources: ocean friction and gravitational twist (two sources, not one). Caricoos. Orbiter-forum. Duration (sec) Velocity. When a Full Moon or New Moon occurs close to the Moon's perigee, it is known as a Supermoon.On the other hand, when a Full Moon or New Moon occurs close to the Moon's apogee, it is known as a Micromoon.. What is the Moon Illusion? Unlike addons, they do not directly influence the game, as they are run separately.. Lunar Orbit Insertion, on the surface, appears to be a standard orbital mechanics problem, solvable using straightforward, albeit sophisticated tools to calculate a solution. Area = 1/2 the base * the height. And of course Kerbal Space Program for motivating me to finally learn orbital mechanics. Celestial bodies have large masses, which are often measured in Earth, Jupiter or Solar masses. Event . At the Google page for "lowest lunar velocity," there is a link at the bottom for a Google search page for "lunar orbital velocity calculator," but when clicking to the page, there's nothing for calculating the moon's velocity. Lunar Perigee and Apogee Calculator Lunar Perigee and Apogee Calculator: Moon calendar the moon calendar of the current month, shows also the phases of the Moon for any month or day from 3999 BC to 3999 AD: Moon Phase Calculator: Moon Phase Calculator Calculate the phases of the Moon: Moon phase pictures: Orbit Velocity Calculator If we observe it from the point of view of the Sun: as we can see detailed in this answer, the orbit of the Moon around the Sun is practically circular: the 400000km orbital radius around the Earth is just a minor perturbation on its $\approx$ 150million km orbit around the Sun. Alcyone Lunar Calculator (ALC) provides detailed astronomical information on the Moon. As the distance to the sun increases to infinity the lunar orbit loses this twist; but without the energy gained from this twist the orbital radius decreases to R' = Rcosø. Calculating a Hohmann Transfer: A Hohmann Transfer is a very common orbital maneuver used by astrophysicists to send a spacecraft from a small circular orbit to a larger one. I feel that this would be a great way to learn the steps required to calculate different Kepler orbital elements of an object, plot orbits, and predict where the object will be at some future time. The velocity has to be just right, so that the distance to the center of the Earth is always the same.The orbital velocity formula contains a constant, G, which is called the "universal gravitational constant". It would be like a dream-come-true for me to have a lunar-velocity calculator. For a given LEO station orbit, there are two launch opportunities per month (when the moon intersects the plan of the station’s orbit). moon orbit calculator, Olex's beautiful Interactive illustrated interplanetary guide and calculator which inspired me to create this tool as a web page. Calculator. I would like to build some orbital mechanical software from scratch. Abstract: Introduction: Lunar Orbital Motion described in Quran: A New Relation in the Earth-Moon System: Abstract: The greatest speed C, denoting the velocity of light in vacuum, is hinted at in two glorious Quranic verses relating this fundamental universal contant C with the motion of … Calculate Orbital Speed. orbital mechanics and the lunar orbit; (b) Write a MATLAB program that will calculate the orbits of the satellite and the moon. Orbital Control of a Satellite Using the Gravity of the Moon ... spacecraft is assumed to start in a circular orbit in the plane of the lunar orbit around the ... used to calculate the variation in velocity, angular momentum, energy and inclination of the spacecraft that realizes this maneuver. This required orbital velocity is less at greater altitudes. 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Chapters 2 –5 dealt with satellite position, velocity, and flight time in an orbit, while Chapter 6 linked a propulsive rocket burn to changes in orbital velocity and mass. This chapter involves altering a satellite’s orbit by applying a propulsive thrust force. As I said earlier, « the Moon's average barycentric orbital speed is 1.010 km/s ». DE405 Lunar Ephemeris Calculator - v2.94 - A PHP Astronomy Program by Jay Tanner Revised: 2019 November 05 at 04:44:23 AM Tuesday2019 November 05 at 04:44:23 AM Tuesday Velocity (ft/sec) Event. This is useful for setting up things like CommNet constellations. Calculating orbital speeds. 7 Impulsive Orbital Maneuvers 7.1 Introduction. speed equals orbital radius times the orbital angular speed The moon is 384,000 km away from the Earth. Change (ft/sec) Apolune (n mi) Perilune (n mi) Lunar orbit insertion ignition You may want to superpose to this velocity the barycentre's velocity about the Sun, which is 29.783 km/s (thus the Moon's velocity about … Exam 2 solutions. Newton's law of gravitation tells us that the force acting on the moon will be $F = \frac{GMm\hat{r}}{r^2}$ All of the mathematical laws provided in the above publication are included in this calculator. A near rectilinear halo orbit (NRHO) is regarded as a potential orbit for a future deep space station that can effectively support sustainable crewed … You can calculate the area swept out each hour. In this Instructable I will walk you, step by step, through calculating the Hohmann Transfer for sending … A Supermoon versus a Micromoon. Fixed. Consequently, to demonstrate regression of lunar nodes, trajectories of both bodies are treated as circles which radiuses equal to semi-major axis of the observed Moon’s orbit ellipse. Use Equation 5 to calculate the answer to question 1. Calculator for the orbital speed, the velocity of a celestial body (planet or moon) around another one (star or planet). This calculation requires the input of 1 user generated variable, being the distance the satellite is from the earth's surface. That computes to about a 9 hour flight. Orbital mechanics calculations I’m trying to analyze transfer trajectories between a station in LEO and one in lunar orbit. So as gravity, orbital velocity is universal space-time property of all space-time entities. This page lists various fan-made tools that can help calculations related to the gameplay of Kerbal Space Program. Specifically, I want to start with calculating the Keplarian elements. Resonant Orbit Calculator For Kerbal Space Program . The effect of all these fascinating dynamics is not to speed the satellite up in its orbit, but to apply a torque (twisting motion) that alters the inclination (tilt) of the plane of the satellite’s orbit. Calculate the resonant orbit needed for a carrier craft to inject craft it carries, like satellites, into equidistant positions of a shared circular orbit. The Moon's phase and the date of its approach to its perigee or apogee are not synced. D. LUNAR FLIGHT It calculates the circular orbital velocity, escape velocity and planetary system escape velocity for the given planet parameters. Find the volumetric mean radius of the moon and then add that to the orbital altitude of the Apollo to calculate R. Don't forget that R in the equation needs to be in meters! … This ellipse calculator comes in handy for astronomical calculations. Astronomy ephemeris app for calculating high precision ephemeris and positions of Sun, Moon and the Planets for engaged amateur astronomers and planetary observers, prefering data and facts instead of pretty picture-apps. At the distance of the Moon it is only about 3,300 feet per second. It calculates accurate geocentric or topocentric positional and physical ephemerides, times and circumstances of lunar events (e.g. Now, if a lunar orbit is circular with the Moon at the center, the satellite travels with constant velocity—a situation that makes it vulnerable to Earth's gravitational pull. It revolves around the earth in 27.3 days. Orbital Velocity & Period Calculation; The orbital velocity formula is a calculation that derives the speed of a satellite that maintains a circular orbit around a astronomical body. Solar and Lunar Orbital Predictions In addition to making orbital predictions of spacecraft, PREDICT can also predict transits of the Sun and the Moon. 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text:
# Require help understanding small angle approximation

## Homework Statement

"In order to simplify problems in physics, we often use various approximations. For example, when we investigate diffraction and interference patterns at small angles θ, we frequently approximate sinθ and tanθ by θ (in radians). Here you will calculate over what range these are reasonable approximations.

For θ= 43° this approximation has an error of almost exactly 10%:

θ = 43.0° = 0.75 radians

sinθ=0.682

|sinθ-θ| / |sinθ| ≈ 10%"

1) For what value of θ (to the nearest degree) is the error in sinθ ≈ θ approximately 5%?
2) For what value of θ (to the nearest degree) is the error in tanθ ≈ θ approximately 5%?
I was recently given this question and very little explanation of the concept. I've struggled with this for a week and read absolutely everything I can find and I'm still not any closer to understanding it. Can anyone please point me in the right direction or explain how to do question 1) and 2)? There are many more questions, but if I can get 1) and 2) down then I should be able to answer the rest by myself. I appreciate any help.

Unsure

## The Attempt at a Solution

Unsure

Related Introductory Physics Homework Help News on Phys.org
The equation at the end explains that |sinθ-θ|/|sinθ| gives the error in approximating sinθ by θ. In other words, it gives the percentage which theta differs from sinθ.

The first question asks: For what values of theta does theta differ from sinθ by less than 5%? in other words:
$\displaystyle \frac{|sinθ-θ|}{|sinθ|}≤.05$

The equation at the end explains that |sinθ-θ|/|sinθ| gives the error in approximating sinθ by θ. In other words, it gives the percentage which theta differs from sinθ.

The first question asks: For what values of theta does theta differ from sinθ by less than 5%? in other words:
$\displaystyle \frac{|sinθ-θ|}{|sinθ|}≤.05$

Thank you, I had been using the equation incorrectly without realising. I have the correct answers now.


text:
# Solutions to Problems 1191–1200

Q1191 Let $ABC$ be a triangle with sides $a,b,c$ in the usual way and let $r$ be its circumradius.

1. Show that $\displaystyle 3r > \frac{a+b+c}{2}.$
2. Let $P$ be any point within $ABC$, and let $r_1$ be the circumradius of $ABP.$  Is it true that $r_1 < r?$


text:
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# In the Sequence x0, x1, x2, ..., xn, each term from x1 to xk

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Re: In the Sequence x0, x1, x2, ..., xn, each term from x1 to xk  [#permalink]

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31 Oct 2013, 01:42
this is wron question which can not be from og. pls, show the question number in which og books.

what is relation between x(k+1) and x (k)

there is no relation and the question is wrong.
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Re: In the Sequence x0, x1, x2, ..., xn, each term from x1 to xk  [#permalink]

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02 Apr 2014, 23:00
3
Here is an algebraic approach in case the GMAT tests us with a similar question where the no of elements are too big to list out and solve.

Since each term in the sequence from X1 to Xk is 3 greater than the previous term, we can right a general formula,

Xk=X0+k*3, inserting the values Xk=15, X0=0
15=0+k*3
k=5

Now each term from Xk to Xn is 3 less than the previous term, the general formula will be

Xn=Xk-(n-k)*3, inserting the values Xn=0, Xk=15, k=5
0=15-(n-5)*3
0=15-3*n+15
3*n=30
n=10

Hope it makes sense
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Re: In the Sequence x0, x1, x2, ..., xn, each term from x1 to xk  [#permalink]

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17 Oct 2016, 15:53
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I got this question as part of 37 timed sample OG questions I created for myself. When I saw it, I got overwhelmed by the wording of the question and decided to blindly guess and skip it. When reviewing my wrong answers, I was able to solve it but it still took me over 3 minutes. I think this is one of the reasons that it is recommended that we solve easy and medium question in less than 1:30, and leave some time for more wordy and time consuming questions like this one. This is a classic example of how a very simple concept can be layered in the GMAT to make it seem more "difficult".
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Re: In the Sequence x0, x1, x2, ..., xn, each term from x1 to xk  [#permalink]

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29 May 2017, 22:27
tonebeeze wrote:
In the sequence $$x_0, x_1, x_2, ... x_n$$, each term from $$x_1$$ to $$x_k$$ is 3 greater than the previous term, and each term from $$x_k_+_1$$ to $$x_n$$ is 3 less than the previous term, where n and k are positive integers and k < n. If $$x_0$$ = $$x_n$$ = 0 and if$$x_k$$ = 15, what is the value of n?

A. 5
B. 6
C. 9
D. 10
E. 15

In this problem, you must stay vigilant and organized. Here we know that the sequence starts at xo = 0 and works its way up to xk = 15.

We then know it decreases from xk+1 to xn = 0 in increments of 3.

So we know that it increases by 3 starting at 0 to 15 (5 steps) and it decreases by increments of 3 from 15 to 0 (5 steps).

5 steps + 5 steps = 10 steps.
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Posts: 49204
Re: In the Sequence x0, x1, x2, ..., xn, each term from x1 to xk  [#permalink]

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28 Mar 2018, 03:37
tonebeeze wrote:
In the sequence $$x_0, x_1, x_2, ... x_n$$, each term from $$x_1$$ to $$x_k$$ is 3 greater than the previous term, and each term from $$x_k_+_1$$ to $$x_n$$ is 3 less than the previous term, where n and k are positive integers and k < n. If $$x_0$$ = $$x_n$$ = 0 and if$$x_k$$ = 15, what is the value of n?

A. 5
B. 6
C. 9
D. 10
E. 15

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/in-the-seque ... 68359.html
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Re: In the Sequence x0, x1, x2, ..., xn, each term from x1 to xk &nbs [#permalink] 28 Mar 2018, 03:37

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tl;dr

• Decrypt the encrypted GPG file found in Outlook Express with the private key stored on the device.

Challenge points: 627
No. of solves: 30
Challenge Author: g4rud4

## Initial Analysis

We are provided with an E01 file(Expert Witness format image). There are a lot of ways in analyzing these files, I choose to use Autopsy for analyzing this. Let’s go ahead and load our E01 file in Autopsy. You can visit Autopsy’s1 documentation if you don’t know how to add a data source to autopsy.

From the description, we have a clue that the terrorist is using a genuine chat client, lets see what all applications are installed in the device.

As we know, all the applications present on the device can be found in Program Files. Some of the applications we need to check are GPG, Mozilla Firefox, NetMeeting, Outlook Express. Let us dig more into it and check if they have identified and configured.

So by checking application data, we can say that Outlook Express and Mozilla Firefox are configured. Let us dig more into them.

## First part solution

As the Outlook Express is configured on the device, it leaves us useful forensics artifacts on the device.

Some of them are the mails received and sent. Whenever we receive a mail or delete a mail or sent a mail it will be stored in a .dbx files. Ex: for Inbox Emails - inbox.dbx, Sent Emails - outbox.dbx etc.

These files are stored at C:\Documents and Settings\Crimson\Local Settings\Application Data\Identities\{random characters}\Microsoft\Outlook Express\

In our case, these are stored at C:\Documents and Settings\Crimson\Local Settings\Application Data\Identities\{72F33BC6-0035-4FE0-AED1-5870C5CA389E}\Microsoft\Outlook Express\

You can see .dbx files being listed there on right. We know that we can’t view the messages stored in DBX files. So I have converted the DBX file into a PDF file using this link. There are other ways too, as this gives us something similar to the GUI, I used this. And one of the best thing is to do strings on the DBX files.

Converting the Inbox.dbx to PDF, One will be able to see that there is a mail from David Banjamin davin.banjamin@gmail.com with a subject Secret File. And a file named secret.gpg has been attached.

We can get this file by a simple keyword search in Autopsy or check below.

So these attached files are stored in this location, unless the user saved it into a specified location C:\Users\{username}\AppData\Local\Microsoft\Windows\Temporary Internet Files\Content.IE5\{random characters}.

We have 4 directories listed there, so rather than traversing through all directories, I used Autopsy’s Web Downloads Result. There we can see that there is a secret.gpg.Zone.identifier file. These Zone identifier files are generated automatically by applications/programs when files are downloaded to a Windows computer. So by checking the Source file path we can get the random characters. So going into that directory(U0PDHEH3), we can get the secret.gpg file easily.

We know that the gpg files can only be decrypted by the Owner’s private key. As we have seen a directory named GPG while traversing through the program files. Going into this directory we can find the secret.key.

Importing the private key and decrypting the encrypted GPG file, we can get the first half of the flag.

$gpg --decrypt secret.gpg Snipping the output, First half: inctf{!h0p3_y0u_L1k3d_s0lv1ng_7h3_F1rs7_p4r7 ## Second part solution As we see that there are a lot of web searches listed out in Web History results in Autopsy and going through them we can see a suspicious link http://35.209.205.103/ in the history. So going to that link there is a login page. And there is a note saying Don’t brutefore the Password. So the password must be saved somewhere. As the terrorist is using firefox. And an active firefox installation will have a profile(in our case - 5ztdm4br.default) which consists of a lot of forensics artifacts and that can be found generally at Path: C:\Documents and Settings\{Username}\Application Data\Mozilla\Firefox\{random characters}.default\ In our case, these are found at Path: C:\Documents and Settings\Crimson\Application Data\Mozilla\Firefox\5ztdm4br.default\ By Checking the Web Form Autofill results in Autopsy or by looking at the formhistory.sqlite database present in the firefox profile, we were able to see that the username as Danial_Banjamin and we need to find out the password. As the username and password are stored in formhistory, that means passwords are stored in firefox saved passwords. We need to decrypt the saved passwords to get the original password. Here comes the interesting part of decrypting Firefox saved passwords. There are a lot of ways 1. By dumping the whole profile and passing the dumped folder location to firepwd2 and a lot more. 2. By dumping only the required files from the profile. I am choosing the second way and here are those files: 1. logins.json - Place where all login information such as encrypted username and password are stored. 2. cert8.db and key3.db/key4.db - These are encrypted SQLite database files, and the entries encryptedUsername and encryptedPassword found in logins.json are encrypted with the keys found in both databases. 3. Permissions.sqlite - It contains permissions for installing add-ons, cookies, etc. After dumping all these files from the firefox profile mentioned above, I used pwdecrypt to decrypt the password. It’s a Debian package and can be installed by with apt. $ sudo apt install libnss3-tools

Then, I used a JSON parser(jq) to parse the JSON file and redirected the output to pwdecrypt.

Here is the json parsed output of logins.json.

$jq . < logins.json { "nextId": 3, "logins": [ { "id": 2, "hostname": "http://35.209.205.103", "httpRealm": null, "formSubmitURL": "http://35.209.205.103", "usernameField": "username", "passwordField": "password", "encryptedUsername": "MDoEEPgAAAAAAAAAAAAAAAAAAAEwFAYIKoZIhvcNAwcECOczOqq7/ZDYBBC7w84JwpxUfkx1Nw52VKlx", "encryptedPassword": "MFoEEPgAAAAAAAAAAAAAAAAAAAEwFAYIKoZIhvcNAwcECCwD7aXJGN+hBDAmr4dSU/2vXn+H+TZDl+oTlLGPMbX4usiAkneTan114d6kB2GGUa2b6771U5YIU40=", "guid": "{3ff55df0-bbb8-4192-98df-a1f428964c31}", "encType": 1, "timeCreated": 1595695030340, "timeLastUsed": 1595858974764, "timePasswordChanged": 1595695030340, "timesUsed": 2 } ], "disabledHosts": [], "version": 2 } As we are having so many entries, and we only need the username, password and URL. So added those entries to json parser and redirected it to pwdecrypt. $ jq -r -S '.logins[] | .hostname, .encryptedUsername, .encryptedPassword' logins.json | pwdecrypt -d .

http://35.209.205.103
Decrypted: "Danial_Banjamin"
Decrypted: "2!6BQ&e626g#YNWxsQWV9^knO8#85*E%6Zaxr@At42"

As the master password was not set by the terrorist we were able to get the decrypted password. So logging in using those credentials gives the second part of the flag.

Second Part of the flag: 4nd_3njoy3d_7he_53c0nd_p4rt_0f_7h3_ch4ll3ng3}

## Flag

By concatinating two parts, here is the final flag:
inctf{!_h0p3_y0u_L1k3d_s0lv1ng_7h3_F1rs7_p4r7_4nd_3njoy3d_7he_53c0nd_p4rt_0f_7h3_ch4ll3ng3}

If you have any queries, Feel free to ping me. I am available on Twitter @NihithNihi

## References

Here are some of the resources I came up while making the challenge. Hope it will be useful.

1. 1.https://sleuthkit.org/autopsy/docs/user-docs/4.3/ds_page.html
2. 2.https://github.com/lclevy/firepwd