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OCDC Article: OCDC, Complaints and Yogi
Published: Oct 1, 2015
OCDC, COMPLAINTS AND YOGI
By: Mark Flanegin, Staff Counsel
Office of Chief Disciplinary Counsel
What can lawyers learn from the wisdom of Lawrence Peter Berra, better known as Yogi Berra? Mr. Berra was one of the best known catchers to play the game of baseball. He was inducted into the National Baseball Hall of Fame in 1972, but is also well known for quotes that have been attributed to him.
Yogi Berra: You got to be very careful if you don't know where you are going because you might not get there.
This article will discuss the initial Office of Chief Disciplinary Counsel (OCDC) complaint process and how attorneys might prevent the filing of a complaint with OCDC. It is intended to assist lawyers from veering off course or taking a costly detour.
Missouri Supreme Court Rule 5.08 provides that the Chief Disciplinary Counsel has the authority, with or without complaint, to investigate any matter of professional misconduct. The majority of complaints are received from clients but complaints also come from judges, other attorneys, family or friends of a client. The office has also opened investigations on information from newspaper articles or news reports.
THE COMPLAINT PROCESS
Complaints submitted to OCDC must be in writing and are reviewed by staff counsel. Not all complaints received result in the opening of a formal investigation. The majority of complaints result in no further action by OCDC because the alleged conduct is not within the jurisdiction of OCDC, or the conduct is determined not to be a violation of the Rules of Professional Conduct. If that is the case, the lawyer is not notified of the complaint.
If a determination is made that a complaint merits further action, OCDC may refer the complaint to its Informal Resolution Program, the Missouri Bar Complaint Resolution Program or initiate a formal investigation.
Investigation File Opened
If an investigation is opened, the lawyer will be asked to respond to the complaint. Whatever the lawyer's initial reaction to the receipt of the complaint (anger, anxiety, disbelief and/or frustration), the lawyer should consider the response as their opportunity to address the specific allegations in a complaint by detailing the work performed on behalf of a client. This can be accomplished by submission of a written narrative addressing the issues raised in the complaint with an explanation of the relevancy of any documents submitted with the response.
Yogi Berra: We made too many wrong mistakes.
Some lawyers decide not to respond at all or they submit copies of documents from the client file with little or no explanation of their relevance. Such action is not beneficial to the lawyer or OCDC. Such action may result in the lawyer spending more time responding to specific requests for information from OCDC. A failure to respond may result in the issuance of a subpoena for the lawyer to visit and discuss the complaint at the office of OCDC.
During the investigation, OCDC may request the lawyer provide additional responses or address specific issues regarding the lawyer's representation.
Lawyers should keep in mind that a failure to respond to OCDC could result in discipline even if the lawyer receives no discipline for the alleged conduct in the initial complaint. Failure to respond to a request for information from OCDC can result in a violation of Rule 4-8.1.
Informal Resolution Program
This program was initiated by OCDC to provide an opportunity to resolve disputes between a lawyer and a client without opening a disciplinary file.
The purpose of the program is to attempt to resolve less serious disputes and maintain the lawyer client relationship. A referral to this program may be made even if the lawyer has concluded the representation of the client. Lack of communication and the failure of the lawyer to return the client file are two of the primary complaints considered for the program. OCDC staff counsel determine what complaints are referred. The lawyer and the complainant cannot request the matter be sent to the program. Complaints that allege serious violations of the Rules of Professional Conduct are not considered for referral.
Yogi Berra: You can observe a lot just by watching.
To paraphrase Mr. Berra, you can learn a lot just by listening. If a complaint is handled through the Informal Resolution Program, the lawyer will be contacted by OCDC. The initial contact is usually by phone. The lawyer will be notified that a complaint has been received and OCDC is attempting to resolve it informally. The goal is to resolve these complaints quickly and without the need to open an investigation. Upon hearing that OCDC is calling in an effort to informally resolve the dispute, the lawyer should understand that prompt attention to the matter could save time and avoid the possible opening of an investigation,
Complaint Resolution Program
This program is administered by the Missouri Bar. Supreme Court Rule 5.10 provides that OCDC can refer complaints that may be best resolved outside of the formal disciplinary proceedings to the Complaint Resolution Program.
Complaints can only be referred to the program by OCDC. Participation in the program by the lawyer and complainant is voluntary. Although a resolution of the complaint might not be reached, the fact that OCDC decided to refer a complaint to the program should be considered as encouragement to participate in the program.
Allegations of serious unethical conduct will not be referred to the program. Complaints most commonly referred by OCDC to the program relate to issues involving communication, diligence and to situations where there may be a misunderstanding between parties.
When a decision is made to refer a complaint to the program, both the lawyer and complainant (either a client or ex-client) are notified in writing by OCDC of that decision. Once the referral is made the OCDC is not involved in efforts to resolve the complaint. Failure of the lawyer to participate in the program may result in OCDC opening an investigation file on the lawyer.
THOUGHTS ON HOW COMPLAINTS MIGHT BE AVOIDED
The majority of complaints received by OCDC involve allegations of a lack of communication or lack of diligence. Whether a client has an unreasonable expectation of how the client's case should be handled or due to concern of what is happening on the case, a lawyer who does not keep clients informed of the status of their case runs the risk of having a complaint filed with OCDC.
Rule 4-1.4 requires a lawyer to keep the client reasonably informed of the status of the matter, promptly comply with reasonable requests for information and explain a matter to the extent reasonably necessary to allow the client to make informed decisions.
During the initial consultation with a client consideration should be given to discussing what the client can expect. This discussion should include what the lawyer can do for the client and address any misunderstandings the client may have. As the case progresses issues regarding pleadings, discovery, scheduled court dates and settlement offers should be discussed with clients.
Clients may file complaints with OCDC alleging lack of diligence even when the lawyer has filed all necessary pleadings, prepared discovery and attended court dates, but has failed to keep the client informed. Lawyers should not avoid direct communication with their clients by relying on support staff to relay messages between the lawyer and client. This may result in the client thinking the lawyer is avoiding them. The prompt return of phone calls and written communication should be considered throughout the representation.
Yogi Berra: Nobody goes there anymore because it's too crowded.
Several factors may explain why a complaint alleging a lack of diligence is filed. Misunderstanding of the legal system by the client, failure of the lawyer to keep the client informed, or lawyer procrastination, to name a few. But also consider the lawyer who fails to recognize a heavy caseload while taking on new clients.
Rule 4-1.3 requires a lawyer to act with reasonable diligence and promptness in representing clients. Too many clients and too little time is a lack of diligence complaint waiting to happen. Although fewer clients might result in fewer fees, a lawyer runs the risk of failing to diligently represent a client and the consequences that will follow, including the possible filing of a complaint with OCDC and the affect the dissatisfaction of a client will have on the lawyer's reputation.
Train Your Support Staff
Yogi Berra: I'm not going to buy my kids an encyclopedia. Let them walk to school like I did.
Rule 4-5.3 requires a lawyer who has direct supervisory authority over a non-lawyer to make reasonable efforts to ensure the conduct of a non-lawyer in the firm is compatible with the professional obligations of the lawyer.
Following the wisdom of Mr. Berra might be risky when it comes to your support staff. Lawyers who fail to inform staff members of the ethical requirements of their employment and supervise staff members run the risk of a client complaint and possible discipline.
A FEW QUESTIONS, A FEW ANSWERS
If a lawyer receives a complaint can the lawyer continue to represent the client?
Yes, the Rules of Professional Conduct do not prohibit a lawyer from continuing to represent the client simply because a complaint was filed. Rule 4-1.16 should be reviewed to determine if withdraw would be appropriate. It is not unusual for lawyers to continue representation of the client during the complaint process.
Can a lawyer agree to a settlement that provides that a party will not file a complaint, withdraw a complaint or not cooperate regarding a complaint filed with OCDC? The Supreme Court Advisory Committee addressed this issue in Formal Opinion 122. The Opinion states:
"It is the opinion of the Advisory Committee that an attorney who enters into, or attempts to enter into, a settlement that includes a term that a party to the agreement will withdraw, refrain from filing, or decline to cooperate regarding, a complaint under Supreme Court Rule 5 violates Rule 4-8.4(d) by engaging in conduct prejudicial to the administration of justice."
The Opinion does provide that the lawyer and complainant involved in a complaint may communicate with each other and attempt to resolve the problems between them.
May a lawyer retain the client file? Complaints received by OCDC regarding this issue often involve the discharge of a lawyer by a client or withdraw of a lawyer, and the client requested the file because the client's legal matter has not been resolved. Rule 4-1.16(d) provides that upon termination of representation, a lawyer should take reasonable action to protect the client's interests, including the surrender of papers and property to which the client is entitled.
The complete file belongs to the client. This includes ""work product."" Items in the file that the lawyer has out of pocket expense may be retained by the lawyer (not the complete file), but only until reimbursement is made. Examples of those items would include depositions and medical records paid for by the lawyer. If the lawyer wants to keep a copy of the file, the lawyer is responsible for the costs of copying the file.
Correspondence from OCDC requesting a response to a complaint should not be ignored. Lawyers should consider it as an opportunity to address the issues raised in the complaint and provide information that may result in the dismissal of the complaint.
A lawyer who is asked to address a dispute through the Informal Resolution Program or the Complaint Resolution Program should seriously consider doing so, as it may prevent the opening of an investigative file.
During the representation of a client time spent on the review of each client's file, the timely performance of the services required for each client and communication with each client may prevent the filing of a complaint with OCDC.
1 All quotes in this article attributed to Yogi Berra are taken from www.baseballalmanac.com.
2 The determination to close an investigation without discipline, the referral of an investigation to a Regional Disciplinary Committee, the issuance of discipline or the filing of an Information with a Disciplinary Hearing Panel is beyond the scope of this article.
See Supreme Court Rule 5.11. If after completion of an investigation there is a finding of probable cause to believe the lawyer is guilty of professional misconduct an admonition may be administered or an Information prepared. Pursuant to Rule 5.08, OCDC may request regional disciplinary committees to investigate matters regarding professional misconduct.
3 Supreme Court Rule 5.09(b)
4 Supreme Court Rule 4-8.1(c)
5 Supreme Court Rule 5.10. See also the Missouri Bar Complaint Resolution Program Guidelines.
6 Supreme Court Rule 5.01. The Missouri Supreme Court Advisory Committee is appointed by the Missouri Supreme Court. The Committee is comprised of lawyers and non-lawyers.
7 Supreme Court Rule 5.30. The Advisory Committee may give Formal Opinions as to the interpretations of Rule 4, 5, and 6.
8 Missouri Advisory Committee Formal Opinion 115, as amended.
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text:
Q: Elasticsearch query to search two word combination with space I have a elasticsearch query to search the data based on name.
My query is
$http.post(elasticSearchURL,{ "filter": { "and": [{ "term": { "Name": "allan" } } ] } })

The above query works fine for single word search but when I give two words with space it doesn't picks any data for it.
My query is not working for below scenario.
{ "filter": { "and": [{ "term": { "Name": "allan edward" } } ] } }

I dont know what keyword should I have to append to satisfy my search scenario.
Thanks in advance

A: Phrase match query is what you are looking for.
A query like below should work fine -
{
    "query": {
        "match_phrase": {
            "title": "allan edward"
        }
    }
}

redpajama_set_name: RedPajamaStackExchange


Can I Use Credit Card Miles to Upgrade My Seat?
Airline Cards or Bank Cards: Which Should You Carry?
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Is There an Alternative to My Airline Credit Card?
Which Credit Cards Reduce the Risk of Losing My Miles?


text:
Actor Dick Anthony Williams Passes Away
by Jennie Mamary Feb. 19, 2012
Dick Anthony Williams, a veteran actor perhaps best known for his role as Pretty Tony in "The Mack," died Thursday in Los Angeles, said his family and friends. The cause was not announced.
Born in Chicago on August 9, 1934, Williams had an extensive career on stage, films and television. Williams' film credits include "Five on the Black Hand Side," "The Jerk," "Mo' Better Blues" and "Edward Scissorhands," among others.
Williams also worked steadily on Broadway, earning Tony nominations for his roles in "What the Wine-Sellers Buy" and "Black Picture Show." He was a series regular on the 1990s drama "Homefront," and was featured in the mini-series "King," "American Playhouse" and "Our Family Honor." Williams had guest roles on episodic TV series such as "Dragnet," "The X-Files," "Martin" and "The Shield."
With Woodie King, Jr., Williams co-founded the New Federal Theatre (NFT) in New York, which showcased a multitude of African-American artists, including Ruby Dee, Ossie Davis, Phylicia Rashad and Denzel Washington, among others.
Williams was preceded in death by his wife, acclaimed actress Gloria Edwards. He is survived by his children, Mona, Jason and Mikah, and a host of family and friends.
Listen: THE BIG ONE-OH! Cast Recording Now Available Digitally
MEAN GIRLS Songs Have Been 'Reinvented' For Movie Musical
Jeff Richmond has given an update on the upcoming film adaption of Mean Girls the musical. Richmond stated that he and his wife, Tina Fey, are working 'day-to-day' on the new movie musical, revealing that the music has been 'reinvented' for the big screen. The film stars Angourie Rice, Auli'i Cravalho, Jaquel Spivey and Reneé Rapp.
Check Out This Week's Top Stage Mags
Take a look at this week's top Stage Mags including productions from Capital Stage, Gaslight Theatre, and more.
Alyssa Fox to Take Over as Elphaba in WICKED Beginning in March
Alyssa Fox will take over the role of Elphaba in WICKED at Broadway's Gershwin Theatre beginning Tuesday, March 7th. See how to purchase tickets!
Alan Cumming Returns OBE, Citing 'Toxicity' in the British Empire
Alan Cumming has taken to Instagram to reveal that he has returned his OBE, due to his feelings about the 'toxicity' of the British Empire.


text:
Morning for the Osone Family
While a bit on the nose and preachy, this also had moments that felt incredibly powerful and real. It's a shame to end the set on a lesser entry, but this was a journey I'm glad I took.
The rest of the films in this set were made while Keisuke Kinoshita was under wartime Japanese censorship laws. This film, made after the war ended, fell under American occupying forces censorship laws.
In some ways, the films Kinoshita made under Japanese laws feel more interesting, at least in the sense that they were forced to tell their stories in extremely oblique ways. This film could be much more direct in its anti-war values, and while I agree with those values, the film loses something as a result.
The story is of one family during the war, and everything bad that happens to them as a result.
The film opens with the arrest of the oldest brother for writing a vaguely anti-war paper. From there we see the ultra-conservative military general uncle of the family forced to move in, and the resulting effect on the mother, daughter, and two remaining sons.
It's a rather bleak story, with very little in the way of positive outcomes.
I'd bet making this film felt like a similar morning for Kinoshita himself. After years of straining against the censorship laws, and after having been effectively baned for making his previous film, the comparative freedom must have been incredible. The dialogue he could suddenly participate in, of how to re-build Japan after centuries of destructive militarism, sounds like a fascinating time to work in.
Other than the tacked-on American happy ending, this is an interesting start in that process, even if it's ultimately not an overwhelming success. - Jun 18th, 2018
japan, 1946, 1.33:1, japanese


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redpajama_set_name: RedPajamaGithub


text:
\section{Introduction}
State estimation in power systems is critical for maintaining normal and secure operating conditions. In power transmission systems, the weighted least squares (WLS) method \cite{Abur2004} is  well developed and widely used by utilities for state estimation; however, the limited availability of measurements renders the WLS inapplicable in  power distribution systems. The requirement for state estimation in  distribution systems is becoming stringent because the increased penetration of distributed energy resources---such as solar photovoltaics, wind turbines, and energy storage systems---on distribution systems introduces bidirectional power flows that might impact the system responses to various types of disturbances.

Much work has been done in an attempt to address the low observability state estimation problem. Reference \cite{Baruki2017} determined the optimal minimum measurement locations and used the difference between the measured and calculated voltages and complex powers to obtain the voltage profile of the whole network. Reference \cite{Rigoni2017} used  the voltage sensitivity at each bus to the load at all buses to determine the voltage given the measured load at each location. References \cite{manitsas2012, Pertl2016,YCNN,zamzam2019data} applied neural networks, which do not require system models, to estimate the voltage in the distribution grid; however, these approaches still require the installation of significant numbers of phasor measurement units (PMUs) when considering large systems. References \cite{manitsas2012,Clements2011, wu2013,zhou2019gradient} used pseudo-measurements, which are estimates based on historical data to overcome the requirement of the installation of more meters; however, it is known that the pseudo-measurements typically have  larger measurement errors than the metered measurements.

An alternative approach that does not require installing new sensors or explicit computation of pseudo-measurements was recently proposed by \cite{Schmitt}. This method leverages the standard matrix completion method \cite{exactMatrixCompletion} and augments it with linearized power flow constraints to acknowledge for the physical network constraints.
This method was shown to be effective in estimating voltage phasors using single-snapshot information.  However, this method requires solving a semidefinite programming (SDP) problem, which becomes computationally infeasible for large systems or if multiple-snapshot (time-series) information is used.

In fact,  temporal correlation (dependency between measurements at different time steps) exists among data in addition to the spatial correlation (dependency between measurements at different locations) and the correlation among measurement types (characterized by  power flow equations). By modeling both the temporal and spatial correlation of the data, \cite{gao_wang2016, Liao2019} apply the standard matrix completion method to recover missing PMU data,  and \cite{Genes2019} applies the standard matrix completion method with Bayesian estimation to recover missing low-voltage distribution system data.

This paper proposes an efficient algorithm to solve the constrained matrix completion problem with time-series data. To this end, this paper formulates  matrix $X$ using time-series data  by considering both the  spatial  and  temporal correlation of the data. Similar to \cite{Schmitt}, this paper leverages a linear approximation of the power flow equations as constraints to characterize the correlation among different measurement types.
Then, this paper applies
the alternating minimization method,  which was a winner in the Netflix Challenge \cite{Koren2009},  to solve the proposed matrix completion problem for state estimation in multiphase distribution systems.

To apply the alternating minimization method,  matrix $X$ is written in a bilinear form, i.e., $X=UV$, and then the algorithm finds the best $U$ and $V$ in an alternating fashion. Because of the bilinear term in the objective function, the problem becomes nonconvex with respect to any variable and thus the alternating minimization method is not guaranteed to converge to the global optima. However,
results on the  convergence of the method were established under some regularity conditions in \cite{Luo1993,xu_yin_2013}. This paper proves that the objective function satisfies these conditions, which guarantee the convergence of the proposed method.

The rest of this paper is organized as follows. Section~\ref{section:ProblemFormulate} introduces the standard matrix completion model, the formulation of the data matrix using time-series data, the linearized power flow constraints, and the full matrix completion model for state estimation in multiphase distribution systems. The alternating minimization algorithm and the  summable convergence are presented in Section~\ref{section:AM}. Simulation results on the IEEE 123-bus system and a real utility feeder are shown in Section~\ref{section:simulationresults}. Section~\ref{section:conclusion} concludes the paper.

\section{Problem Formulation}
\label{section:ProblemFormulate}
This section first reviews the standard matrix completion formulation, and then  introduces how to build the data matrix using the time-series data in multiphase distribution systems. Next, the linearized power flow constraints are introduced. Finally,  the full matrix completion model for state estimation in multiphase distribution systems is derived, which combines the standard matrix completion model with the linear power flow constraints.
\subsection {Standard Matrix Completion}
\label{subsection:SMC}
{Let $M\in\mathbb{R}^{m\times n}$  be the matrix we wish to reconstruct, and let $\Omega$ denote the set of indices for known elements of $M$. Define the observation operator ${P}_\Omega:\mathbb{R}^{m\times n} \rightarrow \mathbb{R}^{m\times n} $ as:
   $ {P}_\Omega(M)_{ij}=M_{ij}$ for $(i,j) \in \Omega$; 0 otherwise.

 The goal is to recover $M$ from ${P}_\Omega(M)$,  under the assumption that $M$ is low rank. Because  the rank function is nonconvex and the tightest convex  relaxation of  the  rank  function is the nuclear norm function  \cite{exactMatrixCompletion}, we consider the following regularized matrix completion model:
 \iffalse
 If the low-rank structure of the matrix is true, we want to find the matrix with the minimum rank that is consistent with the observations, leading to:}
\begin{equation}
\begin{aligned}
& \underset{X\in\mathbb{R}^{m\times n}}{\text{minimize}}
& & \mathrm{rank}(X) \\
& \text{subject to}
& & {P}_\Omega(X)={P}_\Omega(M),
\label{MC}
\end{aligned}
\end{equation}
{where $X$ is the decision variable and rank($X$) is the rank of  $X$.}

{Unfortunately, this formulation is of no practical use because the rank minimization is NP-hard. One approach, proposed by \cite{exactMatrixCompletion}, is to  minimize the nuclear norm instead, which is the tightest  convex relaxation of the rank function. In addition, the measurements are susceptible to noise, and \cite{matrixCompletionWithNoise} proposed a noise-resilient constraint $ ||\mathcal{P}_\Omega(X)-\mathcal{P}_\Omega(M)||_F^2\leq \delta$ $(\delta>0)$.
Denote the nuclear norm of $X$ by}
$||X||_*=\sum_{i=1}^{\text{min}\{m,n\}} \sigma_i(X)$,
\begin{equation}
    ||X||_*=\sum_{i=1}^{\text{min}\{m,n\}} \sigma_i(X),
\end{equation}
where $\sigma_i(X)$ is the $i${th} {largest} singular value of $X$.
Then the new model with convex relaxation and noise-resilience is  formulated as:
\fi
\begin{equation}
\begin{aligned}
\label{relaxedMC}
& \underset{X\in\mathbb{R}^{m\times n}}{\min}
& & ||X||_*+\frac{\mu}{2}||{P}_\Omega(X)-{P}_\Omega(M)||_F^2,
\end{aligned}
\end{equation}
where $X$ is the decision variable, $||X||_*=\sum_{i=1}^{\text{min}\{m,n\}} \sigma_i(X)$ is the nuclear norm of $X$ with $\sigma_i(X)$ denoting the $i${th} {largest} singular value of $X$, and $\mu>0$ is a weight parameter.

\subsection{Matrix Formulation  in Multiphase Distribution Systems}
\label{subsection:matrixformulation}
For the scope of this paper,
we consider a general three-phase distribution network consisting of one slack bus and a given number of multiphase $PQ$ buses.

Matrix completion was shown  effective for state estimation in general three-phase distribution systems by \cite{Schmitt}, which formulated the data matrix $M$ using  single-snapshot information. Considering  the temporal correlation of the data, we set up the data matrix $M$ using time-series data.

 Assume that the voltage phasor and other measurements at the slack bus are known. So we use only  measurements at nonslack buses to form the data matrix. {Let $\mathcal{P}$ denote the set of phases at all nonslack buses and $|\mathcal{P}|$ be the number of all phases at  nonslack buses.}
 The measurements we  use in this matrix are the real and imaginary parts of voltage phasor, voltage magnitude, and the active and reactive power injection at each phase of nonslack buses.  Consider a time series $t=1,\ldots, T$. Let $M^t$ denote the measurement matrix at time $t$ {such that each column represents a phase and each row represents a quantity relevant to the phase. To be specific, for each phase $i\in\mathcal{P}$,
the corresponding column of $M^t$ is of the form:}
\[\begin{aligned}
\left[\Re(v_i),\ \Im(v_i),\ |v_i|,\ \Re(s_i), \ \Im(s_i)\right]^{\intercal},
\end{aligned}\]
where $\Re(\cdot)$ and $\Im(\cdot)$ are the real part and imaginary part of a complex variable, respectively, $\intercal$ is the transpose notation, $v=[v_1,\ldots, v_{|\mathcal{P}|}]^{\intercal}\in\mathbb{C}^{|\mathcal{P}|}$ is the vector containing voltage phasors at each phase of nonslack buses, and $s=[s_1,\ldots, s_{|\mathcal{P}|}]^{\intercal}\in\mathbb{C}^{|\mathcal{P}|}$ is the vector of power injections at each phase of nonslack buses.
{Then the matrix $M$ is constructed by
\begin{equation}
\label{eqn:dataMatrix}
\begin{aligned}
M=\left[M^1;\ M^2;\ \cdots; \ M^{T}\right] \in \mathbb{R}^{m \times n},
\end{aligned}
\end{equation}
where  $T$ is the length of the time  series, and $m = 5T, n=|\mathcal{P}|$.}
Note that the data matrix is not limited to the structure proposed above; it can accommodate any available measurements if these measurements are correlated such that $M$ has the (approximate) low-rank property.

Because the rows and/or columns of the matrix $M$ are related by temporal correlation, spatial correlation, or power flow equations, such a matrix has low rank. Fig.~\ref{singularvalues} shows that the low-rank property holds for the IEEE 123-bus  system with one-time step, two-time step, and three-time step  data formulation.

\begin{figure}
   \centering
   \includegraphics[scale = 0.42, trim= 46 0 0 0, clip]{SVD_plots1.png}
   \caption{Singular  values  of  data  matrices  for  the  IEEE   123-bus  system with one-time step, two-time step, and three-time step  data matrix formulation. The data matrices are of size $5\times260$, $10\times260$, and $15\times260$, respectively. The  bars  show  the  individual  singular values (normalized by the singular value sum), and the circles show the cumulative sums of (normalized) singular values.
   The first four largest singular values comprise 99\% of the singular value sum.}
\label{singularvalues}
\end{figure}

\subsection{Linear Power Flow Constraints} \label{linearLoadFlow}

As in \cite{Schmitt},
we use the linear approximation  of  power  flows  as  constraints  to  characterize the correlation among different measurement types, which provides  more  information  about  the  system,  and  thus  likely  requires fewer  measurements  to  recover  the  matrix  than the standard  matrix  completion  formulation.

Recall that we use  $\mathcal{P}$, $v\in\mathbb{C}^{|\mathcal{P}|}$, and $s\in\mathbb{C}^{|\mathcal{P}|}$  to denote the set of phases, the vector of voltage phasors, and the vector of power injections at  all nonslack buses,
respectively.
 We employ approximations of the form:
\begin{subequations} \label{eq:lin_app}
\begin{align}
v  \; &\approx B \begin{bmatrix} \Re(s) \\ \Im(s) \end{bmatrix} + \: w,  \label{eq:vlin} \\
|v| &\approx C \begin{bmatrix} \Re(s) \\ \Im(s) \end{bmatrix}  +|w|, \label{eq:vmaglin}
\end{align}
\end{subequations}
where the coefficients $B,C\in\mathbb{C}^{|\mathcal{P}|\times 2|\mathcal{P}|}, w\in\mathbb{C}^{|\mathcal{P}|}$ are derived by the power flow linearization methods developed in, e.g., \cite{linearLoadFlow,Christakou2013,Giannakis2016}.
Write (\ref{eq:lin_app}) in the following equivalent form with $A_1,A_2,A_3,A_4,C_1,C_2\in\mathbb{R}^{|\mathcal{P}|\times |\mathcal{P}|}$:
\begin{subequations} \label{eq:lin_app2}
\begin{align}
\Re(v)  \; &\approx [A_1\quad A_2] \begin{bmatrix} \Re(s) \\ \Im(s) \end{bmatrix} + \: \Re(w),  \label{eq:vreallin} \\
\Im(v)  \; &\approx [A_3\quad A_4] \begin{bmatrix} \Re(s) \\ \Im(s) \end{bmatrix} + \: \Im(w),  \label{eq:vimglin} \\
|v| &\approx [C_1\quad C_2] \begin{bmatrix} \Re(s) \\ \Im(s) \end{bmatrix}  +|w|, \label{eq:vmaglin2}
\end{align}
\end{subequations}
where $\Scale[0.9]{[A_1 \quad A_2] = \Re(B),[A_3 \quad A_4]=\Im(B)}$, and $\Scale[0.9]{[C_1\quad C_2]=C}$.

 We use $v^t$, $s^t$ to denote the corresponding $v,  s$ in (\ref{eq:lin_app2}) at time slot $t$. Assume that $v_0$ (the slack bus voltage phasor) and the system topology are the same at different time steps, and then by using the linearization method in  \cite{linearLoadFlow}, $A_1, A_2, A_3, A_4, C_1, C_2$ are the same at different time steps.  Hence, we have the linear approximation of voltage phasor and magnitude at time $t$ in (\ref{eq:lin_app2}) with $v,s$ being replaced by $v^t$ and $s^t$.
 \iffalse
 as: \andrey{don't need to repeat this equation, just refer to (4)}
 \begin{subequations} \label{eq:lin_apptimet}
\begin{align}
\Re(v^t)  \; &\approx [A_1\quad A_2] \begin{bmatrix} \Re(s^t) \\ \Im(s^t) \end{bmatrix} + \: \Re(w),  \label{eq:vreallinseries} \\
\Im(v^t)  \; &\approx [A_3\quad A_4] \begin{bmatrix} \Re(s^t) \\ \Im(s^t) \end{bmatrix} + \: \Im(w),  \label{eq:vimglinseries} \\
|v^t| &\approx [C_1\quad C_2] \begin{bmatrix} \Re(s^t) \\ \Im(s^t) \end{bmatrix}  +|w|. \label{eq:vmaglin2series}
\end{align}
\end{subequations}
\fi

 For simplicity of expression in the sequel, we use the following model to express this linear model at time $t=1,\ldots, T$:
 \begin{equation}
\label{eqn:linmodel}
y\approx Ax+b,
\end{equation}
where: \[y = \begin{bmatrix}
    \Re(v^1)\\
    \Im(v^1)\\
    |v^1|\\
    \vdots\\
    \Re(v^{T})\\
    \Im(v^{T})\\
    |v^{T}|
\end{bmatrix},\  A = \begin{bmatrix}
    A_1 & A_2 & 0 & \cdots & 0 & 0\\
     A_3& A_4 & 0 & \cdots & 0 & 0 \\
   C_1& C_2 & 0 & \cdots & 0  &0\\
    \vdots & \vdots & \vdots & \ddots & 0 & 0 \\
    0 & 0 & 0 & \cdots & A_1 & A_2\\
    0 & 0 & 0 & \cdots & A_3 & A_4\\
    0 & 0 & 0 & \cdots & C_1 & C_2
\end{bmatrix},   \]
\[x= \begin{bmatrix}
    \Re(s^1)^{\intercal}\  \Im(s^1)^{\intercal}\  \ldots\  \Re(s^{T})^{\intercal}\ \Im(s^{T})^{\intercal}\end{bmatrix}^{\intercal},\] and
     \[b =\begin{bmatrix}
    \Re(w)^{\intercal}\  \Im(w)^{\intercal}\ |w|^{\intercal}\ \ldots\  \Re(w)^{\intercal}\ \Im(w)^{\intercal}\ |w|^{\intercal}
\end{bmatrix}^{\intercal}\]
\iffalse
\[x= \begin{bmatrix}
    \Re(s^1)\\
    \Im(s^1)\\
   \vdots\\
    \Re(s^{T})\\
    \Im(s^{T})
\end{bmatrix},
\text{ and}\ b =
   \begin{bmatrix}
    \Re(w)\\
    \Im(w)\\
    |w|\\
    \vdots\\
    \Re(w)\\
    \Im(w)\\
    |w|
\end{bmatrix}
\]
\fi
with $ A\in\mathbb{R}^{3T|\mathcal{P}|\times 2T|\mathcal{P}|},x\in\mathbb{R}^{2T|\mathcal{P}|}$, and $y, b\in\mathbb{R}^{3T|\mathcal{P}|}$.

{The linear model (\ref{eqn:linmodel}) will be incorporated into the matrix completion formulation in the following subsection.}

\subsection{The Regularized Matrix Completion for State Estimation}

{
By incorporating the  linear power flow model (\ref{eqn:linmodel}) into  problem (\ref{relaxedMC}) as a regularization term, we obtain the following optimization problem:
\iffalse
\begin{equation}
\begin{aligned}
\label{constrainedmc}
& \underset{X\in\mathbb{R}^{m\times n}}{\text{minimize}}
& & ||X||_*\\
& \text{subject to}
& & ||\mathcal{P}_\Omega(X)-\mathcal{P}_\Omega(M)||_F^2\leq \delta,\\
& & & |||y-(Ax+b)||_2^2\leq \beta,
\end{aligned}
\end{equation}
where $\beta\geq 0$ is a parameter that can be chosen based on the extent of approximation.
\fi

 \iffalse
 \andrey{I suggest the following:
 \begin{itemize}
     \item Stick with problem (9) everywhere, if this is the problem we are solving.
     \item State this problem already in Section II.A, with general regularization term.
     \item I reformulated a bit  problem (9) below -- check if this makes sense. We don't need to define $X$ again, it was already defined above.
 \end{itemize}
 }
 \fi
 \begin{eqnarray}
 \hspace{-3mm}&{\min} & ||X||_*+\frac{\mu}{2}||{P}_\Omega(X-M)||_F^2 +\frac{\nu}{2}||y-(Ax+b)||_2^2 \nonumber\\
\hspace{-3mm}&\text{over} & X \in\mathbb{R}^{m\times n},y \in\mathbb{R}^{\frac{3}{5}mn},x \in\mathbb{R}^{\frac{2}{5}mn},\nonumber\\
\hspace{-3mm}&\text{s.t.} & \Scale[0.95]{y = \left[
    a_1^{\intercal}X \ \,
    a_2^{\intercal}X\ \,
    a_3^{\intercal}X\,
    \ldots \,
    a_{_{3T-2}}^{\intercal}X\ \,
    a_{_{3T-1}}^{\intercal}X\ \,
    a_{_{3T}}^{\intercal}X
\right]^{\intercal}}, \nonumber\hspace{-3mm}\\
\hspace{-3mm}&&  \Scale[0.95]{x = \left[
   c_1^{\intercal}X\ \,
     c_2^{\intercal}X \,
    \ldots \,
    c_{_{2T-1}}^{\intercal}X\ \,
    c_{_{2T}}^{\intercal}X
         \right]^{\intercal}},\hspace{-3mm} \label{regularizedmc}
 \end{eqnarray}
where, $\nu>0$ is a weight parameter,  $m = 5T, n = |\mathcal{P}|$,
$a_{3(t-1)+i}=e_{5(t-1)+i}$ and $c_{2(t-1)+i}=e_{5(t-1)+3+i}$ are standard basis vectors in $\mathbb{R}^{m}$, in which $t$ denotes the time step number and $i$ denotes the $i$th $a$ or $c$ at the $t$-th time step. For example, if $a_1$, $t =1, i =1$, then, $a_1 = e_1\in\mathbb{R}^m$; if $c_1$, $t=1, i = 1$, then $c_1=e_4\in\mathbb{R}^m$.

 \iffalse

 We consider an approximate way to solve problem (\ref{constrainedmc})
by solving the following  unconstrained problem:
\begin{equation}
\begin{aligned}
\label{centralized_SE}
 \underset{X ,y,x}{\text{minimize}}
\quad &||X||_*+\frac{\mu}{2}||\mathcal{P}_\Omega(X)- \mathcal{P}_\Omega(M)||_F^2\\
& \ +\frac{\nu}{2}||y-(Ax+b)||_2^2.
\end{aligned}
\end{equation}
where    $\mu,\nu>0$ are the penalty parameters, $y$ and $x$ are variables mapped from $X$, and the specific mappings   are:
\[X = \begin{bmatrix}
           \Re(v^1)^{\intercal}\\
           \Im(v^1)^{\intercal}\\
           |v^1|^{\intercal}\\
           \Re(s^1)^{\intercal}\\
           \Im(s^1)^{\intercal}\\
           \vdots\\
           \Re(v^{T})^{\intercal}\\
           \Im(v^{T})^{\intercal}\\
           |v^{T}|^{\intercal}\\
           \Re(s^{T})^{\intercal}\\
           \Im(s^{T})^{\intercal}
         \end{bmatrix}, y = \begin{bmatrix}
    X^{\intercal}a_1\\
    X^{\intercal}a_2\\
    X^{\intercal}a_3\\
    \vdots\\
    X^{\intercal}a_{3T-2}\\
    X^{\intercal}a_{3T-1}\\
     X^{\intercal}a_{3T}
\end{bmatrix},x = \begin{bmatrix}
             X^{\intercal}c_1\\
    X^{\intercal}c_2\\
    \vdots\\
    X^{\intercal}c_{2T-1}\\
    X^{\intercal}c_{2T}
         \end{bmatrix}
\]
with $X\in\mathbb{R}^{m\times n}, y\in\mathbb{R}^{\frac{3}{5}mn}$, and $x\in\mathbb{R}^{\frac{2}{5}mn}$.

\iffalse
\begin{align*}
    a_1 &= \begin{bmatrix} 1 & 0 & 0 & 0 & 0 & 0& \cdots & 0 & 0 & 0\end{bmatrix}^T\in\mathbb{R}^{5T},\\
    a_2 &= \begin{bmatrix} 0 & 1 & 0 & 0 &0 & 0 &\cdots & 0 & 0 & 0 \end{bmatrix}^T\in\mathbb{R}^{5T},\\
    a_3 &= \begin{bmatrix} 0 &  0& 1 & 0 & 0 & 0 & \cdots & 0 & 0 & 0\end{bmatrix}^T\in\mathbb{R}^{5T},\\
    &\ \vdots\\
    a_{3T-2} &= \begin{bmatrix} 0 &  0& 0 & 0 & 0 & 0 & \cdots & 1 & 0 & 0\end{bmatrix}^T\in\mathbb{R}^{5T},\\
    a_{3T-1} &= \begin{bmatrix} 0 &  0& 0 & 0 & 0 & 0 & \cdots & 0 & 1 & 0\end{bmatrix}^T\in\mathbb{R}^{5T},\\
    a_{3T} &= \begin{bmatrix} 0 &  0& 0 & 0 & 0 & 0 & \cdots & 0 & 0 & 1\end{bmatrix}^T\in\mathbb{R}^{5T},\\
    c_1 & =  \begin{bmatrix} 0 &  0& 0 & 1 & 0 & 0 & \cdots & 0 & 0 & 0\end{bmatrix}^T\in\mathbb{R}^{5T},\\
     c_2 & =  \begin{bmatrix} 0 &  0& 0 & 0 & 1 & 0 & \cdots & 0 & 0 & 0\end{bmatrix}^T\in\mathbb{R}^{5T},\\
      &\ \vdots\\
      c_{2T-1} & =  \begin{bmatrix} 0 &  0& 0 &  0 & 0 & 0 & \cdots & 0 & 1 & 0\end{bmatrix}^T\in\mathbb{R}^{5T},\\
      c_{2T} & =  \begin{bmatrix} 0 &  0& 0 & 0 & 0 & 0 & \cdots & 0 & 0 & 1\end{bmatrix}^T\in\mathbb{R}^{5T}.
\end{align*}
}
\fi
\fi

\section{Alternating Minimization for Solving the Full Matrix Completion Model}
\label{section:AM}
This section first  proposes the alternating minimization algorithm for the full matrix completion model in multiphase distribution system state estimation, and then proves the  summable convergence of the proposed algorithm.
\subsection{Alternating Minimization Algorithm}
Any matrix $X\in\mathbb{R}^{m\times n}$ of a rank up to $r$ has a matrix product $X= UV$ form with $U\in\mathbb{R}^{m\times r}$ and $V\in\mathbb{R}^{r\times n}$, and its nuclear norm can be expressed by the Frobenius norm of $U$ and $V$ as follows \cite{Srebro2004}:
{
\begin{equation}
\label{eqn:nucleareqFrobenius}
\begin{aligned}
||X||_*:=\ &\underset{U \in \mathbb{R}^{m \times r},V \in \mathbb{R}^{r \times n}}{\arg\min}\ \frac{1}{2} (||U||_F^2+||V||_F^2) \\
& \quad\ \ \mathrm{s.\,t.~} \quad\quad\quad\
 X=UV.
\end{aligned}
\end{equation}
}%
Note that for sufficiently small $r$ ($r\ll \text{min}\{m,n\}$), using this characterization of the nuclear norm  allows us to dramatically reduce the size of the problem.  We now use (\ref{eqn:nucleareqFrobenius}) to reformulate (\ref{regularizedmc}) as follows:
\begin{eqnarray}
\hspace{-4mm}& \Scale[0.95]{\underset{\substack{U \in \mathbb{R}^{m \times r},\\V \in \mathbb{R}^{r \times n}}}{\min}}&\hspace{-2mm}
\Scale[0.95]{\frac{1}{2} (||U||_F^2+||V||_F^2)+\frac{\mu}{2} ||{P}_\Omega(UV-M)||_F^2}\nonumber\\[-12pt]
\hspace{-4mm}&&\hspace{-2mm}\quad\quad \quad\quad \Scale[0.95]{+\frac{\nu}{2}||f_1(UV)-(Af_2(UV)+b)||_2^2,}\nonumber\\
\hspace{-4mm}&\mathrm{s.t.}&\hspace{-4mm} \Scale[0.86]{f_1(UV) = \left[
    a_1^{\intercal}X \ \,
    a_2^{\intercal}X\ \,
    a_3^{\intercal}X \,
    \ldots \,
    a_{_{3T-2}}^{\intercal}X\ \,
    a_{_{3T-1}}^{\intercal}X\ \,
    a_{_{3T}}^{\intercal}X
\right]^{\intercal}}, \nonumber\\
\hspace{-4mm}&&\hspace{-4mm} \Scale[0.86]{f_2(UV) = \left[
   c_1^{\intercal}X\ \,
     c_2^{\intercal}X \,
    \ldots \,
    c_{_{2T-1}}^{\intercal}X\ \,
    c_{_{2T}}^{\intercal}X
         \right]^{\intercal}},\nonumber\\
\hspace{-4mm}&&\hspace{-4mm} \Scale[0.86]{X =UV.}\label{bilinearmc}
\end{eqnarray}

The alternating minimization algorithm that updates the variables in an alternating fashion is proved to be one of the most accurate and effective methods for solving the matrix completion problem \cite{altminmatcomp}. For our matrix completion formulation in state estimation, the alternating minimization algorithm solves for $U$ and $V$ alternatively while fixing the other factor.
The pseudo-code of the alternating minimization algorithm for the formulation (\ref{bilinearmc}) is given in Algorithm~\ref{Agorthim:AM}.

\begin{algorithm}
 \caption{Alternating Minimization Algorithm for Matrix Completion in Distribution System State Estimation}
 \begin{algorithmic}[1]
 \renewcommand{\algorithmicrequire}{\textbf{Input:}}
 \renewcommand{\algorithmicensure}{\textbf{Initialize:}}
 \REQUIRE Set of known indices $\Omega$, measurement matrix $M$, linear model ${A}, b$, and the number of iterations $N$.

\ENSURE Calculate the rank $r$ singular value decomposition  $[\tilde{U} \tilde{\Sigma} \tilde{V}]=\text{SVD}_r({P}_\Omega(M))$, and set $V^{(0)}={{\tilde{\Sigma}}^{\frac{1}{2}}}\tilde{V}$.
  \FOR {$k = 1,\ldots,N$
  }
\STATE \[
\begin{aligned}
\label{eqn_U_update_centralized}
U^{(k)} &= \underset{\substack{U \in \mathbb{R}^{m \times r}}}{\arg\min}\
||U||_F^2 +\mu ||{P}_\Omega(U{V^{(k-1)}}-M)||_F^2\\
& +{\nu}||f_1(U{V^{(k-1)}})-(Af_2(U{V^{(k-1)}})+b)||_2^2
\end{aligned}
\]

\STATE \[
\begin{aligned}
\label{eqn_V_update_centralized}
V^{(k)}&=\underset{\substack{V \in \mathbb{R}^{r \times n}}}{\arg\min}\
||V||_F^2+{\mu} ||{P}_\Omega(U^{(k)}{V}-M)||_F^2\\
&+{\nu}||f_1(U^{(k)}V)-(Af_2(U^{(k)}{V})+b)||_2^2
\end{aligned}\]
  \ENDFOR
 \RETURN $X=U^{(N)}{V^{(N)}}$
 \end{algorithmic}
 \label{Agorthim:AM}
 \end{algorithm}
\subsection{Convergence of the Alternating Minimization Algorithm}

Because of the bilinear form $X=UV$, problem~(\ref{bilinearmc}) is not jointly convex with respect to any variable.
In general, there is no guarantee that a stationary point of a nonconvex problem will coincide with the global optimum. However, \cite{xu_yin_2013} proved the  summable convergence of the alternating minimization algorithm if the objective function satisfies the following four conditions: 1) it  is  continuous  in  its  domain  and  always bigger  than  negative  infinity;  2) it  has  a Nash equilibrium; 3) it is strongly convex with respect  to  each  variable; and 4) it satisfies the Kurdyka-Łojasiewicz property (please see Definition~2.5 in  \cite{xu_yin_2013} for the definition). We show below that our objective function satisfies these four conditions;  thus, we have the following proposition.

\begin{prop}
The alternating minimization algorithm (Algorithm~1) satisfies the summable convergence, i.e.: \[\sum_{k=1}^{+\infty}||U^{(k+1)}-U^{(k)}||_F+||V^{(k+1)}-V^{(k)}||_F<+\infty.\]
\end{prop}

\iffalse
\begin{align*}
    ||U^{(k+1)}-U^{(k)}||_F^2+||V^{(k+1)}-V^{(k)}||_F^2\leq \\
    ||f(U^{(k+1)},V^{(k+1)})-f(U^{(k)},V^{(k)})||^2
\end{align*}
\fi
\begin{proof}
The objective function $f$ can be written as follows:
\begin{align}
    \label{objfun}
    f(U,V) = &\frac{1}{2} (||U||_F^2+||V||_F^2)+\frac{\mu}{2} ||{P}_\Omega(UV-M)||_F^2\nonumber\\
&\ +\frac{\nu}{2}||f_1(UV)-(Af_2(UV)+b)||_2^2,
\end{align}
where:
\begin{align}
    \label{lastterm}
    &||f_1(UV)-(Af_2(UV)+b)||_2^2\nonumber\\
    =&\Scale[0.9]{\sum\limits_{i=1}^{T}||X^{\intercal}a_{_{3i-2}}-(A_1X^{\intercal}c_{_{2i-1}}+A_2X^{\intercal}c_{_{2i}})-\Re(w)||_2^2}\nonumber\\
    &\ \ \Scale[0.9]{+\sum\limits_{i=1}^{T}||X^{\intercal}a_{_{3i-1}}-(A_3X^{\intercal}c_{_{2i-1}}+A_4X^{\intercal}c_{_{2i}})-\Im(w)||_2^2}\nonumber\\
    &\ \ \Scale[0.9]{+\sum\limits_{i=1}^{T}||X^{\intercal}a_{_{3i}}-(C_1X^{\intercal}c_{_{2i-1}}+C_2X^{\intercal}c_{_{2i}})-|w|||_2^2}
\end{align}
with $X=UV$.

\iffalse
1) The objective function $f(U,V)$ is continuous in its domain, and $\text{inf}_{U,V\in\text{domain}}f(U,V)>-\infty$.

2) Problem~(\ref{step1}) has a Nash point.

3) The objective function $f(U,V)$ is strongly convex with respect to $U$ and $V$, respectively.
\fi

First, the domain of the objective function is $(\mathcal{U},\mathcal{V})=\{(U,V):U\in\mathbb{R}^{m\times r}, V\in\mathbb{R}^{n\times r}\}$.
By the form of $f(U,V)$ in (\ref{objfun}), we have that $f(U,V)$ is continuous in its domain $(\mathcal{U},\mathcal{V})$, and it is non-negative for any $(U,V)\in (\mathcal{U},\mathcal{V})$ .

Second,  to prove that (\ref{bilinearmc}) has a Nash point, we prove that (\ref{bilinearmc}) has a global minimizer, which by definition is a Nash point.  By  the definition of $f(U,V)$ in (\ref{objfun}), the following expression holds:
\[\lim\limits_{\substack{||U||\rightarrow +\infty,\\
||V||\rightarrow +\infty}} f(U,V)=+\infty,\]
which means that $f(U,V)$ is coercive \cite{Lamberscoercive}.
 Then, by Theorem~2 in \cite{Lamberscoercive}, problem (\ref{bilinearmc}) has a global minimizer.

Third, we prove that $f(U,V)$ is strongly convex with respect to $U$ and $V$, respectively.
To prove that $f(U,V)$ is strongly convex with respect to $U$, we prove that $\frac{\partial^2f(U,V)}{\partial U^2}\succ 0$ as follows.

Let $g(U):=||f_1(UV)-(Af_2(UV)+b)||_2^2$ for a fixed $V$. Then we have

\iffalse
\begin{equation}
\label{secondorderder}
    \frac{\partial^2f(U,V)}{\partial U^2}= I_{r\times r}\otimes I_{m\times m}+\mu V^TV\otimes I_{m\times m}+\frac{\nu}{2}\frac{\partial^2g}{\partial U^2}.
\end{equation}
\fi

\begin{align}
    \label{secondorderder}
    \frac{\partial^2f(U,V)}{\partial U^2}= &I_{mr\times mr}+\mu (V\otimes I_{m\times m})^T {R_\Omega} (V\otimes I_{m\times m}) \nonumber\\ &\quad\quad+\frac{\nu}{2}\frac{\partial^2g}{\partial U^2},
\end{align}
where $R_\Omega\in\mathbb{R}^{mr\times mr}$ is the diagonal matrix such that
$(R_\Omega)_{ii}=1$ if  $\big( ( i \mod n) +1, \lceil \frac{i}{m} \rceil \big) \in \Omega$ and 0 otherwise.

By the form of $g$ in (\ref{lastterm}), we  focus only at the second-order partial derivative of the first term in the first summation term in (\ref{lastterm}); treatment of the other terms can be derived similarly. Let $g_1$  denote the first term in the first summation term in (\ref{lastterm}).
\iffalse
Then
\begin{align*}
  \frac{\partial^2g_1}{\partial U^2}&=\\ &\ \frac{\partial^2(c_1^TUV^TA_1^TA_1VU^Tc_1)}{\partial U^2}+\frac{\partial^2(c_2^TUV^TA_2^TA_2VU^Tc_2)}{\partial U^2}\\
  &\ +\frac{\partial^2(a_1^TUV^TVU^Ta_1)}{\partial U^2}+\frac{\partial^2(2c_1^TUV^TA_1^TA_2VU^Tc_2)}{\partial U^2}\\
  &\
   -\frac{\partial^2(2c_1^TUV^TA_1^TVU^Ta_1)}{\partial U^2}-\frac{\partial^2(2c_2^TUV^TA_2^TVU^Ta_1)}{\partial U^2}\\
  &= 2V^TA_1^TA_1V\otimes c_1c_1^T+2V^TA_2^TA_2V\otimes c_2c_2^T\\
  &\ +2V^TV\otimes c_1c_1^T+2V^TA_1^TA_2V\otimes c_1c_2^T\\
  &\ +2V^TA_2^TA_1V\otimes c_2c_1^T-2V^TA_1^TV\otimes c_1a_1^T\\
  &\ -2V^TA_1V\otimes a_1c_1^T-2V^TA_2^TV\otimes c_2a_1^T\\
  &\ -2V^TA_2V\otimes a_1c_2^T.
\end{align*}
It is hard to prove that $\frac{\partial^2g_1}{\partial U^2}\succeq 0_{mr\times mr}$ by the form of $\frac{\partial^2g_1}{\partial U^2}$ in the above equation.
\fi
We will prove that
$g_1$ is a convex function by definition, then using that $g_1:\mathbb{R}^{m\times r}\rightarrow \mathbb{R}$ is convex if and only if $\frac{\partial^2g_1}{\partial U^2}\succeq 0$ to derive that  $\frac{\partial^2g_1}{\partial U^2}\succeq 0$.

By (\ref{lastterm}), we have that:
\[g_1(U) = ||A_1V^{\intercal}U^{\intercal}c_1+A_2V^{\intercal}U^{\intercal}c_{2}-V^{\intercal}U^{\intercal}a_1+\Re(w)||_2^2.\]
Because $\mathcal{U}$ denotes the set of all matrices of size $m\times r$, we have that $\mathcal{U}$ is a convex set.
Then by the form of $g_1(U)$, it is easy to derive that  $\forall U_1, U_2\in \mathcal{U}, \forall t\in [0,1]$: \[g_1(tU_1+(1-t)U_2)\leq tg_1(U_1)+(1-t)g_1(U_2).\]
\iffalse
\begin{align*}
   &g_1(tU_1+(1-t)U_2)\\
    &=||tA_1V^{\intercal}U_1^{\intercal}c_1+(1-t)A_1V^{\intercal}U_2^{\intercal}c_1+tA_2V^{\intercal}U_1^{\intercal}c_2\\
    &\quad +(1-t)A_2V^{\intercal}U_2^{\intercal}c_2-tV^{\intercal}U_1^{\intercal}a_1-(1-t)V^{\intercal}U_2^{\intercal}a_1\\
    &\quad +t\Re(w)+ (1-t)\Re(w)||_2^2\\
    &\leq t||A_1V^{\intercal}U_1^{\intercal}c_1+A_2V^{\intercal}U_1^{\intercal}c_{2}-V^{\intercal}U_1^{\intercal}a_1+\Re(w)||_2^2\\
    &\ \Scale[0.95]{+ (1-t)||A_1V^{\intercal}U_2^{\intercal}c_1+A_2V^{\intercal}U_2^{\intercal}c_{2}-V^{\intercal}U_2^{\intercal}a_1+\Re(w)||_2^2}\\
    &=tg_1(U_1)+(1-t)g_1(U_2).
\end{align*}
\fi

Hence, $g_1$ is convex, implying that $\frac{\partial^2g_1}{\partial U^2}\succeq 0$.

Because all the other terms in (\ref{lastterm}) share the similar form with $g_1$, we can similarly prove that all the other terms in (\ref{lastterm}) are convex functions with respect to $U$; thus, we have that $\frac{\partial^2g}{\partial U^2}\succeq 0.$
By (\ref{secondorderder}), we have that
$I_{mr\times mr}\succ 0$, and $\mu (V\otimes I_{m\times m})^T {R_\Omega} (V\otimes I_{m\times m}) \succeq 0$; therefore, for $\mu>0, \nu>0, \frac{\partial^2g}{\partial U^2}\succeq 0$, we have
$\frac{\partial^2f(U,V)}{\partial U^2}\succ 0.$

Hence, we conclude that $f$ is strongly convex with respect to $U$. The proof that $f$ is strongly convex with respect to $V$ is similar and is omitted for brevity.

By \cite{xu_yin_2013}, any real analytic function satisfies the Kurdyka-Łojasiewicz  property. And by definition of the real analytic function, the objective function (\ref{objfun}) is real analytic; thus, (\ref{objfun}) satisfies the Kurdyka-Łojasiewicz property.

This concludes the proof.
\end{proof}
\iffalse
\april{We can actually do better than square summable.  this section proves that our objective meets the assumptions used in Yangyang Xu's paper, which utilizes the KL property to further show that the norm difference of the iterates is summable }
\yajing{April, that will be great if we can have stronger convergence results. But what I am concerned is whether you can write down the proof this week. Because I am working on the simulation results and we'd better finish the paper writing by the end of this week (the submission deadline is 9/23).}
\april{You've already proved it.  The paper you cite proves iterates are summable in addition to being square summable, so you can just change the wording in the last sentence}
\fi
\section{Simulation Results}
\label{section:simulationresults}
This section demonstrates Algorithm~\ref{Agorthim:AM} on the IEEE 123-bus test system \cite{ieee123} and  a real utility feeder system. The two systems are both three-phase unbalanced radial distribution systems, in which buses are one-, two-, or three-phase. The slack bus is three-phase, and the total number of phases at all buses for the IEEE 123-bus system is 263 and that for the real utility feeder system is 1234. The data for both systems were simulated at 1-minute resolution using power flow analysis with diversified load and solar profiles that were created for each bus using realistic solar irradiance and load consumption data.
The voltage magnitudes range from 0.95 to 1 p.u., and the voltage angles are around 0 or $\pm 120$ degrees.
\vfill
\begin{figure}
   \centering
   \includegraphics[scale=0.45,trim= 80 240 45 240, clip]{convergence.pdf}
   \caption{Convergence of the alternating minimization algorithm with one-time step data matrix formulation and 50\% available measurements.}
\label{convergence}
\end{figure}
\vfill
\begin{figure}
   \centering
   \includegraphics[scale=0.5,trim= 95 210 50 200, clip]{plot_MAPE_MAE1.pdf}
   \caption{Comparison of performance for the alternating minimization algorithm and SDP solver. }
\label{mape_mae_onetime}
\end{figure}

As in Section~\ref{subsection:matrixformulation}, the data matrix is formulated using  the  real and imaginary parts of voltage phasor,  voltage  magnitude,  and active  and reactive power injection at each phase of nonslack buses. We consider  the real and imaginary parts of voltage phasor as variables, and the voltage magnitude,  active power, and reactive power as potentially known measurements. In our experiments, we define the percentage of known measurements as the ratio of the number of known measurements and the total number of voltage magnitude, active power, and reactive power in the data matrix. If less than two thirds of the measurements are known, there are fewer measurements than variables, under which case, the system is underdetermined and the WLS cannot generate a unique solution. For all of our experiments,  the known measurements are added with noise with zero mean and 1\% of the true value as the  standard deviation. And the simulation results are based on the average of $50$ runs for each scenario.
\subsection{Performance on IEEE 123-Bus System}
First, we implement our algorithm with one-time step data formulation at one time slot when solar generations are nonzero with $10\%$ to $70\%$ measurements available (where WLS is under-determined). We compare
the alternating minimization algorithm with the SDP solver used by \cite{Schmitt}. Both algorithms are run with MATLAB on a laptop with 1.9-GHz CPU and 32 GB RAM.

 Fig.~\ref{convergence} shows one representative convergence result (with 50\% available measurements)  of the alternating minimization algorithm.
Fig.~\ref{mape_mae_onetime} shows that the mean absolute percentage errors (MAPEs) of the voltage magnitude  and the mean absolute errors (MAEs) of the voltage angle are comparable for the  alternating minimization algorithm and the SDP solver. The running time for the  alternating minimization algorithm is about 15 seconds  for different percentages of available measurements, whereas that for the SDP solver is more than 70 seconds. These results show that the  alternating minimization algorithm estimates voltage phasors more  computationally efficient than the SDP solver under similar performance. The running time for the SDP solver increases  as more measurements are available. This is  because the SDP solver solves a constrained SDP problem, where more measurements being available means more constraints to be satisfied, and thus longer time is required to achieve the convergence.

\iffalse
\vspace{2mm}
\begin{table}[h]
\begin{center}
{\caption{Average running time over 50 runs for alternating minimization (AM) and SDP solver on a laptop with 1.9 GHz CPU and 32 GB RAM.}
  \label{runtime_123}
            \begin{tabular}{ | l |l | l | l | l | l|p{5mm} |}
                \hline
                {\% Percentage of Measurements Available} & {10}\ & {30}\ & {50}\ & {70}\ & {90}\ \\
                \hline
                {Running time for AM}& {36} & {41} & {42} & {25} & {19}   \\ \hline
                {Running time for SDP Solver}& {78} & {85} & {88} & {89} & {93}\\ \hline
            \end{tabular}
}
        \end{center}
        \end{table}
\fi
\vfill
\begin{figure}
   \centering
   \includegraphics[scale=0.5, trim= 95 200 50 190, clip]{plot_MAPE_MAE2.pdf}
   \caption{Comparison of performance for alternating minimization algorithm on one-time step, two-time steps, and three-time steps. }
\label{mape_mae_timeseries}
\end{figure}
To test the computation  time  and  estimation  accuracy as more data are used, we  implement the  alternating minimization algorithm on the two-time step and three-time step data matrix formulation with $10\%, 30\%, 50\%$, and  $70\%$ measurements available. Fig.~\ref{mape_mae_timeseries} shows that the MAPEs of the voltage magnitudes and the MAEs of the voltage angles for the two-time step and three-time step cases are much better than the one-time step case. This is because the matrix completion problem minimizes the rank, and the larger the time steps are, the smaller the rank of the matrix is compared to its size (which is shown in Fig.~\ref{singularvalues}) and the more accurate the estimates are. The  running time also increases with the length of time steps, however, because of the increased size of the matrices.
The MAPEs of the voltage magnitudes and MAEs of the voltage angles for
the three-time step case is slightly better than the two-time step case overall, but the running time almost doubles. However, the running time for the three scenarios shows that the alternating minimization algorithm for state estimation can be implemented in real time for the IEEE 123-bus system.

\subsection{Performance on A Real Feeder System}
In order to demonstrate the scalability of our algorithm, we implement it on a real utility feeder system with 1234 phases under the assumption that 50\%  measurements are available  for one-time, two-time, and three-time step matrix formulation, respectively. The performance in terms of MAPE, MAE, and running time are shown in Table~\ref{tab:realfeeder}. The results show that the performance improves with more data being used for building the matrix and the computation time also increases. However, the running time shows that the algorithm can be applicable in real-time estimation.
\begin{table}
	\caption{Performance  on a real utility feeder system}\vspace{-10pt}
\label{tab:realfeeder}
	\begin{center}
	\begin{tabular}{l c c c c}
			\toprule
	            & MAPE  & MAE &  Time (s)\\
			\midrule
			One-time step matrix formulation &  $0.4840$ & $0.3967$ & $50$\\
			Two-time step matrix formulation &  $0.4240$ & $0.2869$ & $105$\\
			Three-time step matrix formulation & $0.3503$ & $0.2265$ & $156$ \\
			\bottomrule
		\end{tabular}\vspace{-15pt}
	\end{center}
\end{table}
\section{Conclusions}
\label{section:conclusion}
This paper applied the constrained matrix completion formulation for state estimation in multiphase distribution systems. Different from the constrained matrix completion, the data matrix was formulated using time-series data and  the alternating minimization algorithm was applied to solve the  constrained matrix completion. The  summable convergence of the alternating minimization algorithm was proved. In addition, the efficacy and scalability of the algorithm were demonstrated via the IEEE 123-bus system and a real utility feeder system.

\bibliographystyle{IEEEtran}

redpajama_set_name: RedPajamaArXiv


Indicia title is "FROSTY THE SNOWMAN, No. 661." Code number is FROSTY O.S. #661-5511. Copyright 1956 by Hill & Range Songs, Inc.
Pencils, inks, and colors credits for this sequence from Alberto Becattini (May 14, 2007).
After getting hit by a snowball, Frosty hits a tree with a snowball, dislodging a shower of snow on the boy who hit him.
While Frosty is skating at a pond in the woods, an old witch takes his broom to use for flying.
During a spell of mild weather, Frosty gets a job selling frozen food for a grocery store.
Santa's elves are all down with colds. Frosty rounds up children to finish making the toys so Santa can make his rounds on schedule.
Frosty goes to a gold rush in Chillybone County in the North Woods, where he helps Grandpa Green find gold and captures Black Jack, the robber.
Frosty dresses up as Santa to bring Santa some gifts.
Frosty gets Jack Frost to write farewell messages to the children on their windows when he has to return to the North.
Back cover. Last panel is Dell's "A Pledge to Parents." Pencils, inks, and letters credits for this sequence from Alberto Becattini (May 14, 2007).


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text:
The Ciesla Foundation
Moe Berg (2019)
Rosenwald Film (2015)
Yoo Hoo Mrs. Goldberg (2009)
The Life and Times of Hank Greenberg (1998)
Partisans of Vilna (1986)
Film Credits
DVD Bonus Features Credits
Memories & Stories
About the Filmmaker
Fund Recipients
Augusta Savage: Harp Restoration
Screenings By State
Download Free Teaching Guide
An industrial museum in Chicago: Rosenwald's "Museum of Science and Industry"
by datdudejbal | Jan 31, 2013 | Rosenwald Fund
The Museum of Science and Industry sits near the lakefront on Chicago's South Side, prominently situated within the beautiful Frederick Law Olmsted-designed Jackson Park. It is the only one of the many large neoclassical structures built for the 1893 World's Columbian Exposition that still stands today. The rest of the buildings in what was known as the "White City" were temporary structures, clad in bright white plaster, but the Palace of Fine Arts was a sturdier building, necessarily fireproofed due to its housing of priceless artworks from around the world. This was fortunate, as a large fire claimed the rest of the White City in 1894, just one year after it was completed.
The "White City" of the 1893 World's Columbian Exposition, Palace of Fine Arts visible in right midground
Photo credit: Brooklyn Museum (flickr)
In the early part of the twentieth century, the building served as the temporary home of the Field Museum of Natural History until that museum moved to its permanent location further north along the lakeshore in Grant Park in 1920. It was difficult to find a use for the unoccupied building because of its massive square footage and the necessity of major renovations. The South Park Commission (a governing body over South Side parks) even at one point voted for its demolition. As a Chicago Tribune op-ed put it, "Though a vast structure it is exquisitely graceful. In a state of decay for years, it has been preserved only because no man in authority dared to order it destroyed." (Chicago Daily Tribune, Aug 19. 1926).
Poster advertising the new Museum of Science and Industry
Credit: Work Projects Administration, 1940 (Library of Congress)
As Chicago began preparing to host its second World's Fair in 1933, the "Century of Progress," Julius Rosenwald became interested in establishing a permanent "Industrial Museum" in Chicago to showcase America's history of technological innovation as well as teach the country's youth about how modern technology works. The former Palace of Fine Arts seemed an obvious location as it had space enough for large-scale exhibits, it was owned by the South Park Commission and its graceful neoclassical architecture conveyed the promise of technology to make possible, as the Tribune put it, "our greater material prosperity and our greater leisure" and transform overcrowded and polluted cities into inspiring and recuperative public spaces. "Housing an industrial museum in the midst of classic refinement impresses us as a recognition of the fact that the machine has brought leisure and with leisure a greater opportunity for the cultivation of beauty than the world has ever known" (Tribune, Aug 19, 1926).
Slide of Daniel Burnham's "Plan of Chicago," early example of the "City Beautiful" movement
Photo credit: Penn State Libraries Pictures Collection (flickr)
The White City itself (and the "City Beautiful" movement it helped to spawn) was originally inspired by the beauty and gracefulness of Europe's public buildings and public infrastructure. Likewise, Rosenwald was inspired by the great industrial museums in Paris, London, Vienna and especially Munich to create the Museum of Science and Industry. Rosenwald first visited Munich's Deutsches Museum with his son in 1911. Later, in 1926, as he became more and more committed to creating a similar industrial museum in Chicago, Rosenwald went back to Europe with his family. Along the way, he reported to overseas Tribune correspondents about his vision for Chicago's own museum: "I would like every young growing mind in Chicago to be able to see working models, visualizing developments in machines and processes which have been built by the greatest industrial nation in the world" (Tribune, Apr 17, 1926).
In the 1920s, two other cities in America had industrial museums in the works (Washington D.C. and New York) but with Rosenwald's dedicated support, Chicago's was the first to be completed. The process, however, did not go smoothly, and Rosenwald did not see the museum open before he died. Renovations of the building were complex; most of the exterior was to be replaced with limestone and the interior was a totally new design. Money was also an issue. Rosenwald intended the industrial museum to be funded similarly to his other philanthropic projects, that is, his initial large donation of $3 million would "challenge" others to support the cause. However, the Depression severely limited the ability of others in the community to donate to the fledgling museum. Rosenwald provided most of the monetary support, going as far as to personally guarantee the dividends of the flagging Sears stock he had previously donated to the museum.
When the museum was first incorporated as a non-profit organization, it was called the Rosenwald Industrial Museum. Rosenwald strongly disagreed with it bearing his name, and successfully had it changed to the name we know it as today. Although he had provided virtually all of the cash investment necessary to start the museum, he felt that it should be an ongoing public institution and thus not be associated with his family in perpetuity. Rosenwald's biographer and grandson Peter Ascoli quotes him on this point: "From the very inception of this public project in 1926, I insisted that it should not be named after me… The Museum belongs to the people of Chicago and the nation. Whatever I contributed toward founding the Museum has been in the firm belief that it will play a useful part in our educational, industrial and scientific life. I hope the Museum will enlist the interest and aid of the entire country" (qtd. in Ascoli, 329).
Contemporary photo of the Museum of Science and Industry
Photo credit: Oscar Shen, 2012 (flickr)
Rosenwald's gifts went largely to the substantial renovations of the building; he hoped that its exhibits and upkeep would come from the public. He outlined his vision of corporate donations to a Tribune reporter in 1926: "America has thousands of these historical old models stored away in research laboratories of many of our great industries. These and specially built working models showing the insides of the workings and why the wheels go around should be assembled together and exhibited in a great museum in Chicago" (Tribune, Apr 17, 1926).
Portrait of Rosenwald in Museum's boardroom
Photo credit: Aviva Kempner, 2011
The Museum of Science and Industry opened in stages. Several exhibits were opened to public during the 1933 World's Fair, but the formal opening was not until March 7, 1938 (Ascoli, 379). Over its more than seventy years of existence, the museum has stayed remarkably true to its original vision. Permanent exhibits such as the coal mine, the historical airplanes and the U-Boat were all part of Rosenwald's original concept for the museum. Others, such as the agricultural and train exhibits, were conceived by the original planning committee of the museum before it opened. Although many of the museum's thousands of visitors likely have no knowledge of Julius Rosenwald, his presence is still felt in the museum. Rosenwald's portrait hangs in the museum's boardroom, there is an event and exhibit space called Rosenwald Court, and the museum has organized a "Rosenwald Society" to receive charitable gifts.
Rosenwald Court in the Museum of Science and Industry
We've had two shoots at the Museum of Science and Industry so far for The Rosenwald Schools. Back in 2011, we shot b-roll of the building exterior and Jackson Park. In early December of 2012, we interviewed Kathleen McCarthy, director of exhibits and collections and also filmed the coal mine exhibit, which is still a favorite at the museum.
By Michael Rose
John Mace Grunsfeld, astronaut and Rosenwald descendant, appears on "The Colbert Report"
by Cieslafdn | Aug 10, 2012 | Rosenwald Fund
Astronaut John Mace Grunsfeld was recently on Comedy Central's "The Colbert Report" to talk about NASA's new Mars rover, Curiosity. Curiosity landed on Mars early Monday (August 6th) morning and has already sent back many black and white images. Grunsfeld explained how this rover differs from earlier ones–its chemistry laboratory is much more sophisticated–and talked about its primary mission: finding evidence of historical life on Mars by studying and doing tests on the dirt it recovers.
Grunsfeld's background is linked to Julius Rosenwald in a couple of ways. His grandfather, Ernest Grunsfeld Jr., was Rosenwald's nephew and designed the Adler Planetarium and the Michigan Boulevard Garden Apartments, an innovative apartment complex that housed many famous Chicagoans, including Quincy Jones and Joe Louis.
Also, growing up in Hyde Park, Chicago, Grunsfeld has said he became interested in science early in life through visits to the nearby Museum of Science and Industry, another Rosenwald-funded project that was initially known as the Rosenwald Industrial Museum. Rosenwald was inspired to create the Museum of Science and Industry after seeing similar museums in Vienna and Munich, and his hope was that the exhibits detailing industrial technology would motivate new scientific innovation by museum goers.
You can watch the segment from "The Colbert Report" on Hulu.
Rosenwald Discussion with Hadassah, Birmingham
JULIUS ROSENWALD: INNOVATIVE BUSINESSMAN, VISIONARY PHILANTHROPIST EVENT
Black Education Before Brown
John Lewis: Together, You Can Redeem the Soul of Our Nation
Juneteenth and Questioning a President's Legacy
Pleasant Plains School on the National Register! – Chowan Discovery Group on Rosenwald School spotlight: Pleasant Plains School
September 9: Free Screening of "Rosenwald" In Hillsborough, NC – Center for Documentary Studies at Duke University | CDS Porch on Home
AroundWellington.com » October, 2015 – Rosenwald, the Film on Screenings By State
ROSENWALD, a film by Aviva Kempner | Alice Walker | The Official Website for the American Novelist & Poet on Screenings By State
Aviva Kempner
Ciesla Foundation
Rosenwald Fund
Rosenwald Grant Recipients
Rosenwald Screenings
School Restorations
Social Justice Work
Rosenwald
An Aviva Kempner Film
2018. The Ciesla Foundation


Tis the season! It's time for another great giveaway from one of my favorite places, Pink Slate Boutique!
I loved pairing their Perfect Maxi with a jacket for fall.
They also have so super cute sweaters, like this Young at Heart one.
-An Essie brand mail polish "Set in Stones"
-A Pink Slate Necklace "Jasmine's Jewels"
-A $25 Pink Slate giftcard!
You must be a follower of this blog to enter and the winner will be chosen next Friday! Good luck!
Awesome giveaway! I love you in that maxi dress and denim jacket!
WOWZA!! Great giveaway!!! Thanks a bunch!
You are such a cute pregnant woman. I was going to say beautiful, but you are too funky for that. You just rock these prego clothes. And you look so happy and healthy. It's really great to see.
Love, love, love Pink Slate!!!


And you need to start TM after selected "Watch PC" on the TV, it's not working without that. TM need to be relaunched every time, as the TV doesn't see the TM server without.
pictures are sometimes very small, all made by the same camera.
With video the avi files works fine, but when i will play some HD mp4 files it takes a long time to see the movie on the TV.
I have no problem to restart TMS every time, software version tv 0. 26.58.5 and PMS is 5.1 on a XP machine.
I've an Philips 42PFL8654 with the same featrure "Net TV". Streaming from my TMS 4.4.18 on Synology NAS 1TB works fine. No issues and failure playing mp3's and pictures (no resizing, etc.), starting videos takes a little time before playing.
Good to read that you get at least some perfromance out of your Philips TV.
I've recently bought the 42 inch version of the 8404H series. I've installed TMM 1.0.2.49. as well as the latest media server.
When I have te Media manager running on my pc, I can access the data on the pc from my tv by pulling it from the PC. What I want to do is use TMM to push the data but the Philips is not available as a media player icon. When i go to configurations and select the option to list the available media players, the Philips is listed as a 'generic DLNA 1.0".
What am I missing, how do I get the philips tv to be dispayed in the media player list allowing me to drag and drop movies to the TV?
Hi, I guess no way to get the TV running as an DMR, because it's not 100% DLNA/UPnP compliant , so it would not be able to push media to the PHILIPS TV's (like Sony Bravia or Samsung) with TMM or even TB.
Thats disapointing. Í bought the TV with Twonky in mind. I should have done my home work better I guess. What is the use for a TV which is not 100% DLNA/UpNp compatible ?? why bother at all?
I guess my solution is to buy a zyxel 2500 or equivalent, wil that solve my problem?
Is the 2500 a good wired solution. I have cables throughout the house and do not need a wireless solution?


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To save you the trouble of asking yourself the same question, this post has been broken it down into categories by level of necessity. It may not cover everything, but use it as a general guide to help get you started.
Passport – For obvious reasons!
Travel insurance – Don't fail to get insurance on the 'it won't happen to me' basis. In reality, you never know what's going to happen. Be safe and get some insurance.
Swimwear –You never really know when you're going to jump into a lake, dip in a river, or find a guesthouse with a pool. I found I wear swimwear more than underwear here.
Walking shoes – There are many beautiful walks, long distance treks, view point hikes, and temple steps to walk in Asia. It really is important to have decent walking shoes – go for something sturdy with a good grip.
Respectable clothing (ladies only) – There are so many amazing temples to explore throughout Asia. As a general rule, women must cover their shoulders and knees when entering temples. Be a respectful visitor and adhere to these rules.
Sunscreen – This isn't on my list because you can't buy it in Asia. It is on my list because in Asia, they mostly contain whitening substances. They will protect you all the same, but bleaching your skin probably isn't on your list of things to do whilst travelling.
Raincoat – It does rain sometimes. However, it also stays really hot. So a thin, compact raincoat will do you a world of good when you're out and about because you can still enjoy yourself when the sun goes into hiding.
Clothes – I made the mistake of going on a shopping spree before I got to Asia. My advice: go once you get here! Anything you need, they have for cheap as chips. Depending on where you're from, sometimes even cheaper. I ditched a lot of my clothes from home and shopped at markets here to replenish my wardrobe.
Medicine – Disclaimer: this doesn't refer to specific illnesses or conditions. If you have any repeating or very specific medications then assume this to be on the 'must have' list above. Other than that, there are pharmacies on nearly every corner in Asia and they are always helpful and informative. So leave standard painkillers at home and get what you need along the way.
Sunglasses – I mean, you probably will bring your own, but I wouldn't advise designer ones. There are probably hundreds of thousands of pairs of shades residing at the bottom of seas, lakes, and rivers in Asia. It is so easy to lose a pair while travelling. Cheap and cool ones can be bought everywhere, even in basic mini marts, throughout Asia.
Toiletries – There is no need to buy in bulk at home. Okay, so some of the moisturisers do have whitening substances, but as far as shampoo, razors, deodorant, and soaps go, they have it all here at great prices. Pack what you need in the beginning and top up as you go.
Don't Be Ridiculous – Leave it at Home!
Denim Jeans – I cannot stress enough how little you need this item. Long trousers are okay – think leggings, chinos, thin joggers. But jeans are heavy, take a lot of space, and are hardly weather appropriate when it's hot and humid.
Jewellery – Especially anything valuable or sentimental! Moving around a lot makes it easier to lose tiny items like jewellry. It also makes you a target both to other travellers and locals who don't have much wealth. And honestly, when it's hot wearing any jewellery other than small stud earrings can be extremely uncomfortable.
Washing Line (or any related item) – Southeast Asia is amazing for laundry services. Nearly every guesthouse offers it. You pay cheaply by the kilo and get it back washed, dried, pressed and tagged, and it's all done quickly!
There are plenty of packing hacks and travel gear that can make your time in Southeast Asia easier. For example, think about backpack styles. Some of them open around the sides like a suitcase or open from the top and bottom, some even have wheels! Find the one that works for you. You can also buy packing cubes of all sizes and separate, resealable laundry bags to keep your stuff nicely ordered and accessible within your backpack.
For avid readers, Kindles and e-readers are small and lightweight, with capacity for thousands of books. Or bring your iPad to stream movies on your more relaxing nights. Just remember that plugs may be different and bring the correct adaptors.
You can read a great list of other general Southeast Asia travel tips here, and don't forget to read our expert advice for first timers in Asia.
Well, that should help you start figuring out what to pack for Southeast Asia. Anything you think I missed? Tell us what you must have in your backpack when travelling!
Guest writer Clare Caddick from the UK spent a couple months travelling solo around Thailand, Laos, Cambodia and Vietnam on Stray Asia's Lot Pass. She loves nature and believes there is no such thing as fear in adventure!


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Undying Quotes About The Amazing Wonders Of Medicine
Human beings have dedicated themselves over the years in developing medicines that helps combat deadly ailments. The medical practitioners and scholars are always creative. For instance, syphilis which is in its worst stage is always administered for mercury as the treatment. This has affirmed that modern medicine is always on the rising and development gear. Today, there are multiple lives being saved from deadly ailments and this is fundamental to the peace of mind enjoyed by many today. Below are some of the best and most inspiring medical quotations that will help rejuvenate your hopes for the future medicine.
Centuries ago, Paracelsus said' "Medicine is not only a science; it is also an art. It does not consist of compounding pills and plasters; it deals with the very processes of life, which must be understood before they may be guided." Paracelsus understood more about medicine. In 1500s when there was the German Renaissance, Paracelsus served as a significant medical figure. Basically, the art of healing is not trained or leant in a medical institution.
The other inspiring quote to understand is, "Wherever the art of medicine is loved, there is also a love of humanity." – Hippocrates. This was an inspiring quote from one of the world's best thinkers. His ideologies have always been prominent even today. There are over 60 books in the Hippocratic Corpus and these are part of the oldest medical books in existence. Hippocrates is always perceived and regarded to many as the father of the modern medicine.
The other inspiring quote is from Karl Marx. "Medicine heals doubts as well as diseases." Karl Marx was a devoted Germany philosopher who understood the indispensable power of medicine. These beliefs were anchored in the notion and ideology that medicine could soothe the masses. He believed that all people had the right to healthcare services no matter their social class or status. Karl Marx was unfortunate enough as he suffered from a deadly skin disease and there was no medicine that could ease or jettison his suffering.
"He who studies medicine without books sails an uncharted sea, but he who studies medicine without patients does not go to the sea at all." – William Osler. William was behind the introduction of the Johns Hopkins School of Medicine in 1893. William believed that doctors needed more than medicine books. The only way a doctor can sharpen his or her knowledge in medicine is through interacting and meeting patients regularly.
The above quotes on medicine are to rejuvenate your hopes on future health. You are the one responsible of your health trajectory. Therefore, ensure to eradicate and eliminate the fear for tomorrow.
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