text:
Mildred Marie Medlin
Mildred Marie Buoy Albright Medlin died at the age of 91 at 9:29 PM PST on Monday May 24th 2021.
Millie was born to Jessie and Robert Lloyd Buoy on February 27th, 1930 in LaSalle, Colorado. She was one of 6 kids who moved from Colorado to Washington during the Great Depression. She is survived by her baby sister Virginia McDonald.
Our Mom is also survived by her 6 kids, 5 of whom she had in 5 years. They are Carl Eric, Guy Lamont, Karen Shawndell, Sandra Gay and Deana Marie. Then 10 years later, Michele Marie came along to the disappointment of the first 5. JK. She also had 13 grandkids and 13 great grandkids.
She was a pediatric nurse practitioner who started as a candy striper when she was 15. She went to Deaconess School of Nursing in Spokane, WA from 1948 - 1951. She stopped nursing when she was in her 80's after working with the Oregon Outdoor Schools. The bulk of her career was spent working with different tribes of Native Americans in Oregon, Alaska, New Mexico, Montana and Nevada. She was the Vice President of the AFGE union in Ft. Lewis, WA and lost her position there because of her eternal fight for the rights of others. She was given the nickname of Duck when she was in her last years of working because of her love of the Oregon Ducks.
She had two marriages that both ended in divorce and she got the last laugh by outliving them both. Mom may have not been able to pick men but, well, you can't be good at everything and she was an incredible nurse who had a great laugh.
Mom was complicated as all people are but in the end what we are choosing to remember is that she loved us, Jesus and her church.
In her last year, her daughter Sandy took great care of her and when she died her kids gathered as they could. She left this world listening to her daughter Michele singing "Over the Rainbow" as she drew her last breaths with her son Guy watching on.
If you want to do anything in memory of our Mom, please adopt a dog or a cat. She really loved animals.
To order memorial trees in memory of Mildred Marie Medlin, please visit our tree store.


Why Hire Kim Injury Law, P.C. - Atlanta Personal Injury Lawyer | Kim Injury Law, P.C.
We are a holistic Personal Injury Law Firm that takes into account every aspect of how your injuries have emotionally and physically affected your life and your ability to earn a living.
If you have suffered injuries due to someone else's negligence or recklessness, Kim Injury Law, P.C. will guide you every step of the way and will fight for every dollar that you deserve.
With so much on the line, don't leave your life, your future, and your settlement, in the hands of an insurance company. No matter how convincing their commercials are, know that insurance companies will not calculate the full worth of your injury claim.
The American Association for Justice has gone to great lengths to make public all the tricks of the trade insurance companies use to outright deny your claim, or to delay processing your claim, or egregiously decrease your compensation payment.
To read more about this, the association's documents can be viewed here.
The bottom line is Insurance companies work to protect their bottom line, not yours.
What you need is a legal champion. A qualified, experienced Personal Injury Attorney who has the expertise and knowledge to thoroughly investigate your case and navigate you through all the complexities of the liability legal system. If your case goes to court, you need a strong and skillful advocate to represent you.
But understand that time is of the essence. Every state has its own time frame in which you can put a claim in before the statute of limitations runs out.
In Georgia, the statute of limitations for General Personal Injury claims (vehicular accidents, slip and fall, defective products, etc.) is 2 years from the date of the accident.
I am available to talk with you at any hour, day or night. My hands-on approach ensures your case will get all the attention it deserves. If you've been injured in any type of car accident due to negligence on someone else's part, don't wait to be discharged from the hospital to hire an injury lawyer. I can consult with you right from your hospital bed.
Start your case today with a free and confidential consultation. Call (404) 542-3600 now!


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Tag "Google"
Stadia Pro free December games – Farming Simulator 19, Tomb Raider: Definitive Edition
Google Stadia is now available for Stadia Pro subscribers via the Founders Edition and Premiere Edition. Those who currently have Stadia Pro are able to claim Destiny 2: The Collection
Google Stadia is now available, and the gaming community is trashing it
Google Stadia is now available, and it's a cloud-based gaming platform that allows gamers to play via their TV, desktop, laptop, and select phones. A new launch trailer has been
Google Stadia Review
Google is aiming to make gaming more accessible than ever with Google Stadia, a cloud-based gaming platform where you can play on your TV, desktop, laptop, and select phones. There's
Google Stadia is arriving at gamers' doorsteps on November 19
During the Made by Google event in New York, it was announced that Google Stadia Founder's Edition will begin arriving to gamers on November 19, 2019. What time can Stadia
E3 2019: Game whenever and wherever with Google's Stadia
Gamers of all levels were hoping that this year's E3 would be when the next gen consoles were revealed. While Xbox briefly teased their next console with Project Scarlett, E3
What you need to know about Google's gaming platform, Stadia
The Game Developers Conference (GDC) is typically a place for developers and companies to gather and share best practices and ideas. It is also a place for developers looking for
Google's Call Screening rolling out to original Pixel and Pixel XL
Possibly one of the best features that the Pixel has to offer is the innovative Call Screen. The feature allows your Google Assistant to screen calls from unknown numbers, ask who's
You can now pre-order Google's new Pixel Slate
Google has now officially made the new Pixel Slate available for pre-order through both Google and Best Buy with a release date of November 22, 2018. With 4 different models
Made by Google, the new Pixel 3 and other new products announced
There were absolutely zero surprises today from Google. Today on October 9, 2018, at 8:00 am PST was the heavily anticipated Made By Google event which was rumored for a
Pixel 2 update will fix buzzing issue
Not quite as popular as the last generation, the new Pixel 2 has been plagued with screen and audio issues that have caused some early adopters to remain weary. But
Are Switch preorder sales misleading?
Overall, the hype for the upcoming Nintendo Switch console is positive. There are some concerns about the price and online infrastructure, but the media coverage, as a whole, seems great
Two new Android Wear devices coming early in 2017
Google has confirmed that it will release two new smartwatches powered by Android Wear 2.0 in the first quarter of 2017. Not only will these be the first smartwatches to
Google set to announce its own phone October 4
As if the smartphone market wasn't crowded enough, Google is throwing its hat into the ring on October 4th with the launch of its new phone: the Pixel. An alleged leak
My experiences with four digital assistants
By Kevin Casper Have you used a digital, voice-activated assistant? I've used four. I wanted to share some of my experiences, insights, and comparisons of them. A quick look at
Person fired due to Google April Fools' prank
It's April Fools' Day, and Google shot itself in the foot. It released a new prank feature that added a new button, the Gmail Mic Drop. It's an alternative send
Google's Project Fi is now invite free
Last year Google launched its own cell phone service, Project Fi, in select areas and with select phones. Up until now, you had to be invited to try out the
Google has released Star Wars: The Force Awakens experience, plus VR coming soon
Star Wars mania is getting bigger and bigger as Star Wars: The Force Awakens draws near, and now fans having something more to be excited about. Disney has teamed up
What we learned from the 2015 Google Nexus Event
Google officially announced its new line of products yesterday. Although none of it may have been too much of a surprise due to leaks, it is still good to see
Gmail is saving your email relationships – you're welcome
We have all had that moment of panic. That moment when you accidentaly hit that SEND button on an email when you weren't ready. Maybe you sent it to the wrong
Five things we learned from Google I/O 2015 today
Today marked the start of Google's annual developer conference, I/O. Google announced its plans for the future of Android and its hardware. Here are five of the biggest things we

redpajama_set_name: RedPajamaCommonCrawl


We are very proud of our ever growing school band. We have approx. 35 members from Key Stage 2 playing on instruments including recorders, flute, clarinets , trumpet, xylophones, glockenspiels, keyboard and percussion, double bass and saxophone. All children are welcome to join us whatever their experience of playing an instrument – if they can use a beater they are in!!
The bands meet on Tuesday and Thursday lunch times and during the session we work on pieces for our forthcoming concerts. The pieces we have performed in the past include In Dulce Jubilo, Arrival by Mike Oldfield, Vivaldi's |Spring, Annie's Song and Kalyinka. A concert in the local church at Christmas and in the school in Easter celebrates the work done in Band and Choir all term and shows an amazing standard for children so young.
The confidence, determination and excitement of our band members is a pleasure to see and share. They are an important part of school life and regularly perform in assemblies and school events such as fairs. They reach incredible standards but most importantly enjoy making music together. For many children this is a new experience and not one they had ever even considered!


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IBM & DOE Launch COVID-19 High Performance Computing Consortium
IBM, in collaboration with the DOE, launched the COVID-19 High Performance Computing Consortium. The Consortium will help aggregate computing capabilities from some of the most powerful and advanced computers in the world to help researchers everywhere better understand COVID-19, its treatments and potential cures.
The consortium bring together an unprecedented amount of supercomputing power—16 systems with more than 330 petaflops, 775,000 CPU cores, 34,000 GPUs, and counting—to help researchers everywhere tackle this global challenge. These high-performance computing systems allow researchers to run very large numbers of calculations in epidemiology, bioinformatics, and molecular modeling in hours or days, not weeks, months or years.
Two critically important applications of this compute power could include: developing predictive models to assess how the disease is progressing and modeling new potential therapies and a possible vaccine.
These high-performance computing systems allow researchers to run very large numbers of calculations in epidemiology, bioinformatics, and molecular modeling," writes Dario Gil, Director of IBM Research. "Now we must scale, and IBM will work with our consortium partners to evaluate proposals from researchers around the world and provide access to this supercomputing capacity for the projects that can have the most immediate impact."
Partners within the consortium include: IBM, Lawrence Livermore National Lab (LLNL), Argonne National Lab (ANL), Oak Ridge National Laboratory (ORNL), Sandia National Laboratory (SNL), Los Alamos National Laboratory (LANL), the National Science Foundation (NSF), NASA, the Massachusetts Institute of Technology (MIT), Rensselaer Polytechnic Institute (RPI), Amazon, and Google. IBM will together with partners coordinate efforts across the consortium to evaluate proposals from top institutions, and provide access to HPC capacity for projects that can make the most immediate impact.
This new effort builds on already promising uses of supercomputing to fight COVID-19, and could dramatically accelerate scientific discoveries to combat the pandemic.
Available Resources:
Researchers can apply now at XSEDE for the following supercomputing resources:
U.S. Department of Energy (DOE) Advanced Scientific Computing Research (ASCR)
U.S. DOE National Nuclear Security Administration (NNSA)
U.S. National Science Foundation (NSF)
NASA High-End Computing Capability
MIT/Massachusetts Green HPC Center (MGHPCC)
Supercomputing facilities at DOE offer some of the most powerful resources for scientific computing in the world. The Argonne Leadership Computing Facility (ALCF) and Oak Ridge Leadership Computing Facility (OLCF) may be used for modeling and simulation coupled with machine and deep learning techniques to study a range of areas, including examining underlying protein structure, classifying the evolution of the virus, understanding mutation, uncovering important differences, and similarities with the 2002-2003 SARS virus, searching for potential vaccine and antiviral, compounds, and simulating the spread of COVID-19 and the effectiveness of countermeasure options.
Established by Congress in 2000, NNSA is a semi-autonomous agency within the U.S. Department of Energy responsible for enhancing national security through the military application of nuclear science. NNSA resources at Lawrence Livermore National Laboratory (LLNL), Los Alamos National Laboratory (LANL), and Sandia National Laboratories (SNL) are being made available to the COVID-19 HPC Consortium.
LLNL Lassen
23 PFLOPS, 788 compute nodes, IBM Power9/NVIDIA Volta GV100
28 TF per node
2 x IBM POWER9 CPUs (44 cores) per node
4 x NVIDIA Volta GPUs per node
256 BD DDR4 + 64 GB HBM2 (GPU memory) per node
1600 GB NVMe local storage per node
2 x Mellanox EDR IB (100Gb/s per adapter)
24 PB storage
LLNL Quartz
3.2 PF, 3004 compute nodes, Intel Broadwell
1.2 TF per node
2 x Intel Xeon E5-2695 CPUs (36 cores) per node
128 GB memory per node
1 x Intel Omni-Path IB (100Gb/s)
30 PB storage (shared with other clusters)
LLNL Pascal
0.9 PF, 163 compute nodes, Intel Broadwell CPUs/NVIDIA Pascal P100
11.6 TF per node
2 x NVIDIA Pascal P100 GPUs per node
256 GB memory + 32 HBM2 (GPU memory) per node
1 x Mellanox EDR IB (100Gb/s)
LLNL Ray
1.0 PF, 54 compute nodes, IBM Power8/NVIDIA Pascal P100
256 GB + 64 GB HBM2 (GPU memory) per node
1.5 PB storage
LLNL Surface
506 TF, 158 compute nodes, Intel Sandy Bridge/NVIDIA Kepler K40m
3 x NVIDIA Kepler K40m GPUs
256 GB memory + 36 GB GDDR5 (GPU memory) per node
1 x Mellanox FDR IB (56Gb/s)
LLNL Syrah
108 TF, 316 compute nodes, Intel Sandy Bridge
64 GB memory per node
1 x QLogic IB (40Gb/s)
LANL Grizzly
15.2 PB storage
LANL Snow
445 TF, 368 compute nodes, Intel Broadwell
LANL Badger
SNL Solo
The NSF Office of Advanced Cyberinfrastructure supports and coordinates the development, acquisition, and provision of state-of-the-art cyberinfrastructure resources, tools and services essential to the advancement and transformation of science and engineering. By fostering a vibrant ecosystem of technologies and a skilled workforce of developers, researchers, staff and users, OAC serves the growing community of scientists and engineers, across all disciplines. The most capable resources supported by NSF OAC are being made available to support the COVID-19 HPC Consortium.
Operated by the Texas Advanced Computing Center (TACC), Frontera provides a balanced set of capabilities that supports both capability and capacity simulation, data-intensive science, visualization, and data analysis, as well as emerging applications in AI and deep learning. Frontera has two computing subsystems, a primary computing system focused on double precision performance, and a second subsystem focused on single-precision streaming-memory computing.
Operated by the San Diego Supercomputer Center (SDSC), Comet is a nearly 3-petaflop cluster designed by Dell and SDSC. It features Intel next-generation processors with AVX2, Mellanox FDR InfiniBand interconnects, and Aeon storage.
Stampede 2
Operated by TACC, Stampede 2 is a nearly 20-petaflop HPC national resource accessible to thousands of researchers across the country, including to enable new computational and data-driven scientific and engineering, research and educational discoveries and advances.
Operated by the Pittsburgh Supercomputing Center (PSC), Bridges provides an innovative HPC and data-analytic system, integrating advanced memory technologies to empower new modalities of artificial intelligence based computations, bring desktop convenience to HPC, connect to campuses, and express data-intensive scientific and engineering workflows.
Operated by a team led by the Indiana University Pervasive Technology Institute, Jetstream is a configurable large-scale computing resource that leverages both on-demand and persistent virtual machine technology to support a wide array of software environments and services through incorporating elements of commercial cloud computing resources with some of the best software in existence for solving important scientific problems.
NASA's High-End Computing Capability (HECC) Portfolio provides world-class high-end computing, storage, and associated services to enable NASA-sponsored scientists and engineers supporting NASA programs to broadly and productively employ large-scale modeling, simulation, and analysis to achieve successful mission outcomes.
NASA's Ames Research Center in Silicon Valley hosts the agency's most powerful supercomputing facilities. To help meet the COVID-19 challenge facing the nation and the world, HECC is offering access to NASA's high-performance computing (HPC) resources for researchers requiring HPC to support their efforts to combat this virus.
Transform research data into valuable insights and conduct large-scale analyses with the power of Google Cloud. As part of the COVID-19 HPC Consortium, Google is providing access to Google Cloud HPC resources for academic researchers.
As part of the COVID-19 HPC Consortium, AWS is offering research institutions and companies technical support and promotional credits for the use of AWS services to advance research on diagnosis, treatment, and vaccine studies to accelerate our collective understanding of the novel coronavirus (COVID-19). Researchers and scientists working on time-critical projects can use AWS to instantly access virtually unlimited infrastructure capacity, and the latest technologies in compute, storage and networking to accelerate time to results. Learn more here.
MIT is contributing two HPC systems to the COVID-19 HPC Consortium. The MIT Supercloud, a 7-petaflops Intel x86/NVIDIA Volta HPC cluster, is designed to support research projects that require significant compute, memory or big data resources. Satori, is a 2-petaflops scalable AI-oriented hardware resource for research computing at MIT composed of 64 IBM Power9/Volta nodes. The MIT resources are installed at the Massachusetts Green HPC Center (MGHPCC), which operates as a joint venture between Boston University, Harvard University, MIT, Northeastern University, and the University of Massachusetts.
The Rensselaer Polytechnic Institute (RPI) Center for Computational Innovations is solving problems for next-generation research through the use of massively parallel computation and data analytics. The center supports researchers, faculty, and students a diverse spectrum of disciplines. RPI is making its Artificial Intelligence Multiprocessing Optimized System (AiMOS) system available to the COVID-19 HPC Consortium. AiMOS is an 8-petaflop IBM Power9/Volta supercomputer configured to enable users to explore new AI applications.
IBM Research WSC
The IBM Research WSC cluster consists of 56 compute nodes, each with dual socket 22 core CPU and 6 GPUs, plus seven additional nodes dedicated to management functions. The cluster is intended to be used for the following purposes: client collaboration, advanced research for government-funded projects, advanced research on Converged Cognitive Systems, and advanced research on Deep Learning.
56 AC922 nodes
2 x POWER9 CPU per node, 22 cores per CPU
6 x NVIDIA V100 GPUs per node (336 total)
512 GiB DRAM per node
1.4 TB NVMe per node
2 x EDR InfiniBand per node
2 PB GPFS distributed storage
(No local disk)
CUDA 10.1
IBM PowerAI 1.6
IBM HPC Software stack (CSM/JSM/LSF job management; Spectrum MPI
; XL C/C++/FORTRAN 16.1
; GPFS)


text:
Nella mitologia greca, Bremusa è un'Amazzone che faceva parte del contingente con il quale Pentesilea, regina delle Amazzoni, prestò soccorso ai Troiani dopo la morte di Ettore. È ricordata da Quinto Smirneo nel libro I del Posthomerica.

Il mito

Origini
Bremusa era una delle dodici fanciulle guerriere che accompagnarono la loro sovrana Pentesilea, figlia di Ares, presso la città di Priamo, allorché la regina dovette purificarsi per l'omicidio involontario della sorella Ippolita. Pentesilea e il suo contingente di Amazzoni pervennero a Troia nel momento in cui in città vi era lutto per la morte di Ettore, abbattuto da Achille. Alla loro vista, l'anziano Priamo avvertì un leggero sentimento di sollievo che lo distrasse dalla perdita del figlio e provvide a ricompensare Pentesilea con grandi doni.

Nella guerra di Troia
Dopo una notte di riposo nella reggia del sovrano, Pentesilea condusse le Amazzoni in campo aperto per affrontare gli Achei e ricacciarli verso le loro navi. Nello scontro che seguì, la regina delle Amazzoni fece strage di avversari, ma perdette una dopo l'altra tutte le compagne che facevano parte del suo contingente.

Bremusa, che pure si batteva con valore nella mischia, venne trafitta alla mammella destra dalla lancia di Idomeneo, che la privò così della vita; lanciando un ultimo gemito, l'Amazzone si accasciò al suolo rendendo l'anima, come, riporta Quinto Smirneo, un albero di frassino che è abbattuto dalla scure di un boscaiolo che cade con un secco rimbombo.

Bibliografia
 Quinto Smirneo, Posthomerica, libro I, versi 43, 247 ss.

Amazzoni
Partecipanti alla guerra di Troia
Personaggi della Posthomerica

redpajama_set_name: RedPajamaWikipedia


SHINE is a summer camp for young women (ages 12-18). It was created to help show these young ladies what their role is in the church, how to be leaders within that role, and to help them build valuable relationships while they do it!
The camp is held each year during the second week of July; Sunday afternoon through Thursday. If you are a teenage girl, mark your calendars and make plans to attend!
Parents or youth ministers that would like more information are welcome to call the church office at 325-695-0055.


A National Medical and Wellness Tourism Board has been constituted to provide a dedicated institutional framework to take forward the cause of promotion of Medical and Wellness Tourism including Ayurveda and any other format of Indian system of medicine covered by Ayurveda, Yoga, Unani, Siddha and Homeopathy (AYUSH).
India as a destination for Ayurveda is also promoted through the Global Incredible India campaign and by the Indiatourism offices through participation in trade fairs, promotional events, roads hows and seminars.
The Ministry of Tourism has recognised Medical and Wellness Tourism including Ayurveda as a Niche product in order to overcome the aspect of 'seasonality' and to promote India as a 365 days' destination and attract tourists with specific interest.


Partnering with financial services organizations in attracting, recruiting, hiring and on-boarding top Life and Annuity talent including: VP Underwriting, Director Underwriting, Chief Underwriter, Underwriter, Medical Director, Competitive Intelligence, Actuary, and New Business.
Chris graduated from Southeastern Community College with an Associate of Arts Degree.
I had a very good experience with MRI and in particular with Chris Meyer. Chris was very helpful and informative. I appreciate his knowledge of the industry. I am very happy with the end result.
Chris has a great feel for our company and the type of candidates we look for. I have also found Chris to be very trustworthy in our dealings, responsive to our needs and excellent communicator.
Chris is awesome. He went above and beyond to help me with my concerns. Very honest and ethical!


Well people have been talking and wondering, who are the New York Boys Choir? We got the answer for you right here. The New York Boys Choir under the direction of Yitzy Bald is proud to present their knockout debut album. This is the same Yitzy Bald who brought us hit albums like LeGabay, Pruzbul, Mendy Wald's first two albums (Sameach & Lechaim) and even stellar hits for both MBD and Avraham Fried and many more. Now Yitzy is making the transition from solo artists to choirs. The only way Yitzy saw that as being possible was for him to direct the choir himself. Hence the NYBC was created. What to expect? As Yitzy says "Let the album speak for itself". It will be like no other choir out there to date. The album features 12 brand new Yitzy Bald compositions that were composed and arranged specifically for this amazing choir. So this Purim its time to welcome the new choir on the block, the New York Boys Choir.


text:
\section{Introduction}\label{sec1}

Quantum entanglement is a key resource in many quantum information processing (QIP) tasks \cite{book}, such as quantum teleportation \cite{teleportation1,teleportation2}, quantum superdense coding \cite{superdense}, quantum key distribution  \cite{distribution}, quantum algorithms \cite{algorithm}, and measurement-based quantum computation \cite{one-way}.  In particular, depending on the requirement of a specific task, the preparation and the manipulation of multiqubit entangled states with different multipartite features (for instance, the Greenberger--Horne--Zeilinger  \cite{GHZ}, Dicke \cite{Dick}, $W$ \cite{W}, and cluster states \cite{cluster}) are needed, and these different types of entangled states cannot be converted into each other by using local operations and classical communications.  However, there are still theoretical and experimental challenges in study of multipartite entanglement due to the more complex mathematical form and rapidly growing resource overhead with the number of particles increasing.
In recent years,  the weblike property of the $W$-state, due to its robustness against particle loss and decoherence effects, has rendered it to be a useful resource for quantum communication \cite{fujii2011robust}.  Indeed, the $W$-state has been shown to be relevant for many schemes and applications ranging from its use in the foundation of quantum mechanics \cite{test,mattar2017experimental,wu2014robust}, in anonymous quantum networks \cite{network}, in quantum telecloning and teleportation \cite{telecloning},  in quantum computation \cite{cloning-machine,Ai}, in quantum memories \cite{choi2010entanglement} and as a probe for reading information \cite{guha2013reading}.

So far, many theoretical proposals  and realistic experiments  for generating small-size $W$ states have been proposed \cite{exp-W1,exp-W2,exp-W3}.
Currently, there are two efficient ways to generate large-scale photonic  $W$ states: expansion and fusion. Both schemes have now been achieved in a wide range of physical settings \cite{optics1,optics2,ion,NMR}. In 2008, Tashima \emph{et al}. \cite{optics1} proposed a scheme for locally expanding any polarization-based $n$-photon $W$ ($|W_n\rangle$) state to an $(n+2)$-photon $W$ ($|W_{n+2}\rangle$) state by accessing just one of the qubits with a success probability of $(n+2)/(16n)$. This scheme was subsequently  demonstrated experimentally in 2010 \cite{demonstrated}. Schemes for  expanding $|W_n\rangle$ locally to $|W_{n+1}\rangle$ with a success probability of $(n+1)/(5n)$ were also proposed in 2009 \cite{expand2009}, and even one for $|W_n\rangle$ to $|W_{n+k}\rangle$ was proposed in 2011 \cite{expand2011}. Notably, the success probability of the expansion from $|W\rangle_n$ to $|W_{n+k}\rangle$ decreases with an approximately exponential dependence with increasing $n$.

Fusion, on the other hand, was first proposed in 2011 by \"{O}zdemir \emph{et al}. \cite{Ozdemir}.  The idea was to join $|W_n\rangle$ and $|W_m\rangle$ to give the $|W_{n+m-2}\rangle$ with a success probability of $(n+m-2)/(nm)$.
In 2013, enhancement the $W$-state fusion process was proposed through the use of a Fredkin gate, Bugu \emph{et al}. \cite{Bugu} then proposed a mechanism to fuse $|W_n\rangle$ and $|W_m\rangle$ with one ancillary single photon into $|W_{n+m-1}\rangle$ with a success probability of $(n+m-1)/(mn)$. In 2014, Ozaydin \emph{et al}. \cite{Ozaydin} generalized the setup for fusing three $W$ states: $|W_n\rangle$, $|W_m\rangle$, and $|W_t\rangle$ states and one ancillary single photon were joined  into $|W_{n+m+t-3}\rangle$ with a success probability of $(n+m+t-3)/(mnt)$ with a Fredkin gate. Using three CNOT gates and one Toffoli gate, Yesilyurt \emph{et al}. \cite{Yesilyurt} further generalized the scheme for creating $|W_{n+m+t+z-4}\rangle$ from $|W_n\rangle$, $|W_m\rangle$, $|W_z\rangle$, and $|W_t\rangle$ states with a success probability of $(n+m+t+z-4)/(mntz)$. However, the success probabilities of the required CNOT \cite{KLM,1/9,1/41,1/42},  Toffoli \cite{Toffoli0,Toffoli1,Toffoli,Toffoli2,Toffoli3}, and Fredkin \cite{Fredkin1,Fredkin,Fredkin2,Fredkin3,Fredkin4} gates with linear optical elements were generally not considered. Currently, nonlinear fusion schemes for fusing $|W_n\rangle$ and $|W_m\rangle$ into $|W_{n+m}\rangle$ without qubit loss have also been proposed \cite{loss,Gaoting}.

In this paper, we propose a protocol for fusing $W$ states of arbitrary size into a larger one via nonunitary partial-swap gates. By introducing auxiliary spatial degrees of freedom and using $(n-1)$ partial-swap gates, a $|W_{nm-n+1}\rangle$ state can be created from $n$ arbitrary-sized $|W_m\rangle$ states. All the ``garbage''  states are recyclable, and our scheme avoids failed outcomes. Moreover, additional ancillary photon is not required for our scheme. The length (cost or complexity) of our scheme (measured by the number of the two-qubit entangling gates needed to construct the scheme) is much less than the Fredkin- and CNOT-Toffoli-based schemes \cite{Bugu,Yesilyurt}.

\begin{figure}[htpb]
\begin{center}
\includegraphics[width=7 cm,angle=0]{Fusion.pdf}
\caption{Schematic diagram of the proposed scheme for fusing two $|W_3\rangle$ states into a larger one $|W_5\rangle$. The fusion gate operates on the two qubits in the dashed blue rectangle.}  \label{Fusion}
\end{center}
\end{figure}

\section{Simplifying a fusion-based $W$ state with nonunitary partial-swap gate} \label{sec2}

\subsection{Fusion of $|W_n\rangle$ and $|W_m\rangle$ to give $|W_{n+m-1}\rangle$ }

Suppose Alice and Bob possess $n$- and $m$-partite polarization encoded $W$ states, $|W_n\rangle_A$ and $|W_m\rangle_B$, respectively, and they wish to fuse their states together. A schematic example for the fusion  process of two three-partite $W$-states is depicted in Fig. \ref{Fusion}. The entangled $W$-states of Alice ($|W_n\rangle_A$)  and Bob ($|W_m\rangle_B$) can be written as
\begin{eqnarray}              \label{eq1}
\begin{split}
|W_n\rangle_A=(|(n-1)_H\rangle_a|1_V\rangle_1+\sqrt{n-1}|W_{n-1}\rangle_a|1_H\rangle_1)/\sqrt{n},
\end{split}
\end{eqnarray}
\begin{eqnarray}              \label{eq2}
\begin{split}
|W_m\rangle_B=(|(m-1)_H\rangle_b|1_V\rangle_2+\sqrt{m-1}|W_{m-1}\rangle_b|1_H\rangle_2)/\sqrt{m},
\end{split}
\end{eqnarray}
where $|(N-k)_H\rangle_i|k_V\rangle_j$ represents the superposition of all possible permutations of $N-k$ photons with a horizontal polarization ($H$) in mode $i$ and $k$ photons with a vertical polarization ($V$) in mode $j$. Captial letters $A$ and $B$ label the $W$ states are held by Alice and Bob, respectively. Therefore, the initial state of the system composed of Alice and Bob can be written as
\begin{eqnarray}              \label{eq3}
\begin{split}
|W_n\rangle_A\otimes|W_m\rangle_B=
&\frac{1}{\sqrt{nm}}                |(n-1)_H\rangle_a|(m-1)_H\rangle_b|1_V\rangle_1|1_V\rangle_2\\
&+\frac{\sqrt{m-1}}{\sqrt{nm}}       |(n-1)_H\rangle_a|W_{m-1}\rangle_b|1_V\rangle_1|1_H\rangle_2\\
&+\frac{\sqrt{n-1}}{\sqrt{nm}}       |W_{n-1}\rangle_a|(m-1)_H\rangle_b|1_H\rangle_1|1_V\rangle_2\\
&+\frac{\sqrt{(n-1)(m-1)}}{\sqrt{nm}}|W_{n-1}\rangle_a|W_{m-1}\rangle_b|1_H\rangle_1|1_H\rangle_2.
\end{split}
\end{eqnarray}

\begin{figure}[htpb]
\begin{center}
\includegraphics[width=8 cm,angle=0]{w2.pdf}
\caption{Fusion gate for fusing two $W$ states of arbitrary size to obtain a larger $W$ state. The circle ``$\circ$'' denotes $|H\rangle$, signifying that the states of the two photons in modes 1 and 2 will be exchanged if the photon in mode 1 is the $H$-polarized states, and has no effect otherwise. $D_1$ and $D_2$ are single-photon detectors.} \label{w2}
\end{center}
\end{figure}

\begin{table}[htb]
\centering\caption{Truth table of the polarization partial-swap gate.}
\begin{tabular}{ccccc}

 \toprule

 $x_1x_2$      &   $\rightarrow$    &  $y_1y_2$  &        \\

\midrule

  $H_1H_2$          &        &  $H_1H_2$      \\
  $H_1V_2$          &        &  $V_1H_2$      \\
  $V_1H_2$          &        &  $V_1H_2$      \\
  $V_1V_2$          &        &  $V_1V_2$      \\

\bottomrule
\end{tabular}\label{Truth}
\end{table}

As shown in Fig. \ref{w2}, the fusion of $|W_m\rangle_A$ and $|W_n\rangle_B$ states into a larger $W$ state is achieved by sending photons in  mode 1 (2), i.e., $|1_H\rangle_1$ and $|1_V\rangle_1$ ($|1_H\rangle_2$ and $|1_V\rangle_2$), into the partial-swap gate and those in  mode a (b) are kept intact at Alice's (Bob's) site.  Note that the partial-swap gate swaps the states of the two photons if the first photon is $H$ polarization, and has no effect otherwise (see Table \ref{Truth}). That is, the action of this gate on the four input states yields
\begin{eqnarray}              \label{eq4}
\begin{split}
&|1_H\rangle_1|1_H\rangle_2 \xrightarrow{\text{p-swap}} |1_H\rangle_1|1_H\rangle_2,\quad|1_H\rangle_1|1_V\rangle_2 \xrightarrow{\text{p-swap}} |1_V\rangle_1|1_H\rangle_2,\\
&|1_V\rangle_1|1_H\rangle_2 \xrightarrow{\text{p-swap}} |1_V\rangle_1|1_H\rangle_2,\quad|1_V\rangle_1|1_V\rangle_2 \xrightarrow{\text{p-swap}} |1_V\rangle_1|1_V\rangle_2.
\end{split}
\end{eqnarray}
Therefore, such partial-swap gate completes the transformation
\begin{eqnarray}              \label{eq5}
\begin{split}
|W_n\rangle_A\otimes|W_m\rangle_B\rightarrow
&\frac{1}{\sqrt{nm}}                |(n-1)_H\rangle_a|(m-1)_H\rangle_b|1_V\rangle_1|1_V\rangle_2\\
&+\frac{\sqrt{m-1}}{\sqrt{nm}}       |(n-1)_H\rangle_a|W_{m-1}\rangle_b|1_V\rangle_1|1_H\rangle_2\\
&+\frac{\sqrt{n-1}}{\sqrt{nm}}       |W_{n-1}\rangle_a|(m-1)_H\rangle_b|1_V\rangle_1|1_H\rangle_2\\
&+\frac{\sqrt{(n-1)(m-1)}}{\sqrt{nm}}|W_{n-1}\rangle_a|W_{m-1}\rangle_b|1_H\rangle_1|1_H\rangle_2\\
=\;&\frac{\sqrt{n+m-1}}{\sqrt{nm}}|W_{n+m-1}\rangle_{a,b,2}|1_V\rangle_1+\frac{\sqrt{(n-1)(m-1)}}{\sqrt{nm}}\\&\times|W_{n-1}\rangle_a|W_{m-1}\rangle_b|1_H\rangle_1|1_H\rangle_2.
\end{split}
\end{eqnarray}
The photon in mode 1 is then measured in the $\{|H\rangle,\; |V\rangle\}$ basis.  From Eq. (\ref{eq5}), one  sees that (i) When the photon in mode 1 is $V$-polarized and detector $D_1$ clicks, the scheme is successful with probability (success probability) of $(n+m-1)/(nm)$, and the system collapses into the desired state
\begin{eqnarray}              \label{eq6}
\begin{split}
\frac{\sqrt{n+m-1}}{\sqrt{nm}}|W_{n+m-1}\rangle_{a,b,2}.
\end{split}
\end{eqnarray}
(ii) When the photon in mode 1 is $H$-polarized state and detector $D_2$ clicks, then the remaining photon collapses into state  $|W_{n-1}\rangle_a\otimes|W_{m-1}\rangle_b\otimes|1_H\rangle_2$ with probability (recycle probability) of $(n-1)(m-1)/(nm)$.  It is interesting to see that the ``garbage'' state $|W_{n-1}\rangle_a\otimes|W_{m-1}\rangle_b$ of Alice and Bob remains a $W$ state but with a reduced number of qubits, and therefore this state can be recycled, much like a repeat-until-success scheme \cite{lim2005repeat}. Remarkably, the fail probability of the designed scheme is zero in principle as the system can not collapse into the failure states, such as $|(n-1)_H\rangle_a|(m-1)_H\rangle_b|1_V\rangle_2$.

In Table \ref{table1}, we compare our scheme with previous protocols. Here the success probabilities of the Fredkin, Toffoli, CNOT, and partial-swap gates are disregarded. The linear optical entangling gates are inherently probabilistic. The optimal cost of a Fredkin or Toffoli gate is five two-qubit gates \cite{Optimal1,Optimal2}, therefore, the complexity of our partial-swap-based scheme is much lower than the Fredkin-based one \cite{Bugu} and the Toffoli-CNOT-based one \cite{Fu-T}.  Moreover, extra ancillary photon is necessary for the schemes presented in Refs. \cite{Bugu,Fu-T}, and is not required in our scheme.  Remarkably, our protocol is less complex with a higher success probability than any of the other protocols for the generation of a larger $W$ state with the same size \cite{Ozdemir,Bugu,Fu-T}.

\begin{table}[htb]
\centering \caption{Quantum resource required and success probability of various protocols for creating a larger $W$ state. $H$ is an extra ancillary $H$-polarized photon required for the fusion program.}
\begin{tabular}{cccccc
\toprule
 Proposed                           &   Initial                  &       Success  &      Success         &  Recycle                 & Fail          \\
protocol                           &    state                   &        result  &      probability     &  probability             & probability  \\
\midrule
with $I$ \cite{Ozdemir}             &   $W_{m}, W_{n} $          &  $W_{m+n-2}$   &  $\frac{m+n-2}{mn}$  &  $\frac{(m-1)(n-1)}{mn}$ &  $\frac{1}{mn}$ \\
with 1 Fredkin \cite{Bugu}          &   $W_{m}, W_{n}, H $       &  $W_{m+n-1}$   &  $\frac{m+n-1}{mn}$  &  $\frac{(m-1)(n-1)}{mn}$ &  0              \\
with 1 Toffoli, 1 CNOT \cite{Fu-T}  &   $W_{m}, W_{n}, H $       &  $W_{m+n-1}$   &  $\frac{m+n-1}{mn}$  &  $\frac{(m-1)(n-1)}{mn}$ &  0              \\
ours with 1 partial-swap            &   $W_{m}, W_{n} $          &  $W_{m+n-1}$   &  $\frac{m+n-1}{mn}$  &  $\frac{(m-1)(n-1)}{mn}$ &  0  \\
\bottomrule
\end{tabular}\label{table1}
\end{table}

\subsection{Fusing $n$ arbitrary-sized $|W_m\rangle$ states into a large-scalable $|W_{nm-n+1}\rangle$ state}

Fig. \ref{w3} displays a scheme for fusing $|W_n\rangle_A$, $|W_m\rangle_B$, and $|W_t\rangle_C$ states into $|W_{n+m+t-2}\rangle$ by using two partial-swap gates.  We denote polarization-based entangled $W$ states of Alice, Bob, and Charlie as
\begin{eqnarray}              \label{eq7}
\begin{split}
|W_n\rangle_A=(|(n-1)_H\rangle_a|1_V\rangle_1+\sqrt{n-1}|W_{n-1}\rangle_a|1_H\rangle_1)/\sqrt{n},
\end{split}
\end{eqnarray}
\begin{eqnarray}              \label{eq8}
\begin{split}
|W_m\rangle_B=(|(m-1)_H\rangle_b|1_V\rangle_2+\sqrt{m-1}|W_{m-1}\rangle_b|1_H\rangle_2)/\sqrt{m},
\end{split}
\end{eqnarray}
\begin{eqnarray}              \label{eq9}
\begin{split}
|W_t\rangle_C=(|(t-1)_H\rangle_c|1_V\rangle_3+\sqrt{t-1}|W_{t-1}\rangle_c|1_H\rangle_3)/\sqrt{t}.
\end{split}
\end{eqnarray}

As shown  Fig. \ref{w3}, after Alice, Bob, and Charlie send one of their photons ($|1_H\rangle_1$ and $|1_V\rangle_1$, $|1_H\rangle_2$ and $|1_V\rangle_2$, $|1_H\rangle_3$ and $|1_V\rangle_3$) to the two partial-swap gates through modes 1, 2, and 3, respectively, the two partial-swap gates lead to the following transformations:
\begin{eqnarray}              \label{eq10}
\begin{split}
|W_n\rangle \otimes &|W_m\rangle \otimes |W_t\rangle\\\rightarrow&
\frac{1}{\sqrt{nmt}}                     |(n-1)_H\rangle_a|(m-1)_H\rangle_b|(t-1)_H\rangle_c|1_V\rangle_1|1_V\rangle_2|1_V\rangle_3\\
&+\frac{\sqrt{n-1}}{\sqrt{nmt}}            |W_{n-1}\rangle_a|(m-1)_H\rangle_b|(t-1)_H\rangle_c|1_V\rangle_1|1_V\rangle_2|1_H\rangle_3\\
&+\frac{\sqrt{m-1}}{\sqrt{nmt}}            |(n-1)_H\rangle_a|W_{m-1}\rangle_b|(t-1)_H\rangle_c|1_V\rangle_1|1_V\rangle_2|1_H\rangle_3\\
&+\frac{\sqrt{t-1}}{\sqrt{nmt}}            |(n-1)_H\rangle_a|(m-1)_H\rangle_b|W_{t-1}\rangle_c|1_V\rangle_1|1_V\rangle_2|1_H\rangle_3\\
&+\frac{\sqrt{(n-1)(m-1)}}{\sqrt{nmt}}     |W_{n-1}\rangle_a|W_{m-1}\rangle_b|(t-1)_H\rangle_c|1_H\rangle_1|1_V\rangle_2|1_H\rangle_3\\
&+\frac{\sqrt{(n-1)(t-1)}}{\sqrt{nmt}}     |W_{n-1}\rangle_a|(m-1)_H\rangle_b|W_{t-1}\rangle_c|1_V\rangle_1|1_H\rangle_2|1_H\rangle_3\\
&+\frac{\sqrt{(m-1)(t-1)}}{\sqrt{nmt}}     |(n-1)_H\rangle_a|W_{m-1}\rangle_b|W_{t-1}\rangle_c|1_V\rangle_1|1_H\rangle_2|1_H\rangle_3\\
&+\frac{\sqrt{(n-1)(m-1)(t-1)}}{\sqrt{nmt}}|W_{n-1}\rangle_a
|W_{m-1}\rangle_b|W_{t-1}\rangle_c|1_H\rangle_1|1_H\rangle_2|1_H\rangle_3.
\end{split}
\end{eqnarray}

\begin{figure}[!h]
\begin{center}
\includegraphics[width=9 cm,angle=0]{w3.pdf}
\caption{Fusion gate for fusing three $W$ states of arbitrary size to obtain a larger $W$ state.} \label{w3}
\end{center}
\end{figure}

Eq. (\ref{eq10}) implies the following four possible outcomes:

(i) When the photon in mode 1 is $V$-polarized state,  the photon in mode 2 is also $V$-polarized state and detectors $D_1$ and $D_3$ click,  the system collapses into the successful  state $|W_{n+m+t-2}\rangle$
\begin{eqnarray}              \label{eq11}
\begin{split}
|W_{n+m+t-2}\rangle=
&\frac{1}{\sqrt{nmt}}                      |(n-1)_H\rangle_a|(m-1)_H\rangle_b|(t-1)_H\rangle_c|1_V\rangle_3\\
&+\frac{\sqrt{n-1}}{\sqrt{nmt}}            |W_{n-1}\rangle_a|(m-1)_H\rangle_b|(t-1)_H\rangle_c|1_H\rangle_3\\
&+\frac{\sqrt{m-1}}{\sqrt{nmt}}            |(n-1)_H\rangle_a|W_{m-1}\rangle_b|(t-1)_H\rangle_c|1_H\rangle_3\\
&+\frac{\sqrt{t-1}}{\sqrt{nmt}}            |(n-1)_H\rangle_a|(m-1)_H\rangle_b|W_{t-1}\rangle_c|1_H\rangle_3.
\end{split}
\end{eqnarray}

(ii) When the photon in mode 1 is $H$-polarized state, the photon in mode 2 is also $H$-polarized state and detectors $D_2$ and $D_4$ click,  the system collapses into the recyclable state
\begin{eqnarray}             \label{eq12}
\frac{\sqrt{(n-1)(m-1)(t-1)}}{\sqrt{nmt}}|W_{n-1}\rangle_a|W_{m-1}\rangle_b|W_{t-1}\rangle_c|1_H\rangle_3.
\end{eqnarray}

(iii) When the photon in mode 1 is $H$-polarized state, the photon in mode 2 is $V$-polarized state and detectors $D_2$ and $D_3$ click,  the system  collapses into the ``garbage'' state
\begin{eqnarray}             \label{eq13}
\frac{\sqrt{(n-1)(m-1)}}{\sqrt{nmt}}|W_{n-1}\rangle_a|W_{m-1}\rangle_b|(t-1)_H\rangle_c|1_H\rangle_3.
\end{eqnarray}
We call this case ``a partial recyclable''  because the states between Alice and Bob remain a $W$-state but Charlie needs to prepare a new $W$ state for the subsequent round of the fusion process.

(iv) When the photon in mode 1 is $V$-polarized state, the photon in mode 2 is $H$-polarized state and detectors $D_1$ and $D_4$ click,  the system collapses into the ``garbage'' state
\begin{eqnarray}             \label{eq14}
\begin{split}
\frac{\sqrt{(t-1)(m+n-2)}}{\sqrt{nmt}}|W_{n+m-2}\rangle_{a,b}|W_{t-1}\rangle_c|1_H\rangle_3.
\end{split}
\end{eqnarray}
We call this case ``a partial success''  because the state between Alice and Bob has been fused but not Charlie.

Fig. \ref{wn} shows a scheme for fusing multiple $W$ states of arbitrary size simultaneously.
Table \ref{table2} compares the success and failure probabilities and an estimation of the required quantum resources for our proposal against previous schemes.
Compared with other proposals for generating a $W$ state of given size, our proposal scores a higher success probability and a lower failure probability, with a simpler network.

\begin{table}[htb]
\centering \caption{Quantum resources required and success probabilities of various protocols for fusing multiple $W$ states into a larger one simultaneously. $F=((5-m-n-z-t)-(n-1)(m-1)(t-1)(z-1))/(mntz)$.}
\begin{tabular}{cccccc
\toprule
 Proposed                          &  Initial         &       Achieved    &  Success                  &   Fail                          \\
protocol                          &   state          &        state     &  probability              &   probability                     \\
\midrule
with 1 Fredkin \cite{Bugu}         &  $W_m,W_n,W_t,H$ &  $W_{m+n+t-3}$    &  $\frac{m+n+t-3}{mnt}$    &   $\frac{(t-1)(m+n-2)+1}{mnt}$  \\

ours with 2 partial-swaps          & $W_m,W_n,W_t,$      &  $W_{m+n+t-2}$    &  $\frac{m+n+t-2}{mnt}$    &   0 \\

with 1 Toffoli, 3 CNOTs \cite{Yesilyurt}  &  $W_m,W_n,W_t,W_z$   &  $W_{m+n+t+z-4}$  &  $\frac{m+n+t+z-4}{mntz}$ &   $F$ \\

ours with 3 partial-swaps          &  $W_m,W_n,W_t,W_z$   &  $W_{m+n+t+z-3}$  &  $\frac{m+n+z+t-3}{mntz}$ &  0    \\

\bottomrule
\end{tabular}\label{table2}
\end{table}

\begin{figure}[!h]
\begin{center}
\includegraphics[width=12 cm,angle=0]{wn.pdf}
\caption{Fusion gate for fusing $n$ arbitrary-sized $W$ states simultaneously.} \label{wn}
\end{center}
\end{figure}

\section{Linear-optics fusion-based $W$ state using auxiliary spatial degrees of freedom}\label{sec3}

\begin{figure}[!h]
\begin{center}
\includegraphics[width=8 cm,angle=0]{p-swap.pdf}
\caption{Linear-optical post-selected partial-swap gate.
HWP$^{45^\circ}$ is a half-wave plate (HWP) rotated by 45$^\circ$ to induce the transformation $|H\rangle \leftrightarrow|V\rangle$.
Setting HWP$^{22.5^\circ}$ (HWP$^{67.5^\circ}$) to 22.5$^\circ$ (67.5$^\circ$) completes
$|H\rangle\leftrightarrow(|H\rangle+|V\rangle)/\sqrt{2}$ and $|V\rangle\leftrightarrow(|H\rangle-|V\rangle)/\sqrt{2}$ ($|H\rangle\leftrightarrow(-|H\rangle+|V\rangle)/\sqrt{2}$ and $|V\rangle\leftrightarrow(|H\rangle+|V\rangle)/\sqrt{2}$).} \label{p-swap}
\end{center}
\end{figure}

Based on Sec. \ref{sec2}, one can see that the key component of our fusion gates is the partial-swap gate described by  Eq. (\ref{eq4}). The matrix form of this partial-swap gate in the basis $\{|1_H\rangle|1_H\rangle$, $|1_H\rangle|1_V\rangle$, $|1_V\rangle|1_H\rangle$, $|1_V\rangle|1_V\rangle\}$ can be written as
\begin{eqnarray}             \label{eq15}
N_{\text{p-swap}}=\left(
  \begin{array}{cccc}
    1 & 0 & 0 & 0 \\
    0 & 0 & 0 & 0 \\
    0 & 1 & 1 & 0 \\
    0 & 0 & 0 & 1 \\
  \end{array}
\right).
\end{eqnarray}
Obviously, this operation is not a unitary one due to $NN^\dagger \neq N^\dagger N \neq I$, with $I$ being an identity matrix.

The nonunitary gate can be implemented by utilizing the framework of quantum measurement, or by expanding the state space to a larger one, and then performing a proper unitary operation and an orthogonal measurement in the enlarged space in succession.  Here, we employ auxiliary spatial degrees of freedom introduced by polarizing beam splitters PBS$_1$  and PBS$_2$ (see Fig. \ref{p-swap}) to implement the nonunitary polarization partial-swap gate. Next, we provide a step-by-step description of our protocol for implementing this partial-swap gate.

We consider photons 1 and 2 as being initially prepared in an arbitrary two-qubit polarization-encoded state
\begin{eqnarray}              \label{eq16}
\begin{split}
|\psi_0\rangle=&\alpha_1 |1_H\rangle_{in}|1_H\rangle_{in'} + \alpha_2 |1_H\rangle_{in}|1_V\rangle_{in'} \\
&+\alpha_3 |1_V\rangle_{in}|1_H\rangle_{in'} + \alpha_4 |1_V\rangle_{in}|1_V\rangle_{in'}.
\end{split}
\end{eqnarray}

In the first step,  as shown in Fig. \ref{p-swap}, photons 1 and 2 pass through PBS$_1$  and PBS$_2$, respectively.
Next, photons in modes 1, 3, and 4 interact with half-wave plates (HWP) oriented at $45^\circ$ (HWP$^{45^\circ}$), $67.5^\circ$ (HWP$^{67.5^\circ}$), and $22.5^\circ$ (HWP$^{22.5^\circ}$), respectively.  The PBSs and HWPs cause the state to evolve from $|\psi\rangle_0$ to
\begin{eqnarray}              \label{eq17}
\begin{split}
|\psi_1\rangle=&\frac{1}{\sqrt{2}}(
  \alpha_1 |1_V\rangle_1(|1_H\rangle_4+|1_V\rangle_4)
 +\alpha_2 |1_V\rangle_1(|1_H\rangle_3+|1_V\rangle_3)\\
&+\alpha_3 |1_V\rangle_2(|1_H\rangle_4+|1_V\rangle_4)
 +\alpha_4 |1_V\rangle_2(|1_H\rangle_3+|1_V\rangle_3)).
\end{split}
\end{eqnarray}
A PBS  transmits the $H$-polarized and reflects the $V$-polarized components. Therefore, PBS$_1$ and PBS$_2$ impart the spatial  degrees of freedom of the incident photon.  The
HWPs oriented at $45^\circ$ (denoted HWP$^{45^\circ}$) induce the qubit-flip operation $|1_H\rangle \leftrightarrow |1_V\rangle$
while the HWP$^{67.5^\circ}$ results in
\begin{eqnarray}                  \label{eq18}
\begin{split}
&|1_H\rangle \leftrightarrow\frac{1}{\sqrt{2}}(-|1_H\rangle+|1_V\rangle), \quad
|1_V\rangle\leftrightarrow\frac{1}{\sqrt{2}}(|1_H\rangle+|1_V\rangle).
\end{split}
\end{eqnarray}
Finally, the HWP$^{22.5^\circ}$  completes the transformation
\begin{eqnarray}                  \label{eq19}
\begin{split}
&|1_H\rangle\leftrightarrow\frac{1}{\sqrt{2}}(|1_H\rangle+|1_V\rangle), \qquad
|1_V\rangle\leftrightarrow\frac{1}{\sqrt{2}}(|1_H\rangle-|1_V\rangle).
\end{split}
\end{eqnarray}

In the second step, the photons in modes 2 and 3 are  then mixed at PBS$_3$ before going through HWP$^{67.5^\circ}$ while the photons in modes 1 and 4 are mixed at PBS$_4$ before going through HWP$^{22.5^\circ}$. The completion of these operations leads to the joint state
\begin{eqnarray}              \label{eq20}
\begin{split}
|\psi_2\rangle=&\frac{1}{2\sqrt{2}}(
   \alpha_1 (|1_H\rangle_7-|1_V\rangle_7)(|1_H\rangle_7+|1_V\rangle_7+|1_H\rangle_8-|1_V\rangle_8)\\
& +\alpha_2 (|1_H\rangle_7-|1_V\rangle_7)(-|1_H\rangle_5+|1_V\rangle_5+|1_H\rangle_6+|1_V\rangle_6)\\
&+\alpha_3  (|1_H\rangle_5+|1_V\rangle_5)(|1_H\rangle_7+|1_V\rangle_7+|1_H\rangle_8-|1_V\rangle_8)\\
& +\alpha_4 (|1_H\rangle_5+|1_V\rangle_5)(-|1_H\rangle_5+|1_V\rangle_5+|1_H\rangle_6+|1_V\rangle_6)).
\end{split}
\end{eqnarray}

In the third step, the photons in modes 5 and 8 (6 and 7) are combined at PBS$_5$ (PBS$_6$), and the photon in mode 10 (12) passes through HWP$^{45^\circ}$ (HWP$^{45^\circ}$). The operations  $\text{PBS}_5 \rightarrow \text{HWP}^{45^\circ}$ and $\text{PBS}_6 \rightarrow \text{HWP}^{45^\circ}$ make $|\psi\rangle_2$ become
\begin{eqnarray}              \label{eq21}
\begin{split}
|\psi_3\rangle=&\frac{1}{2\sqrt{2}}(
  \alpha_1  (|1_H\rangle_{11}-|1_H\rangle_{12}) (|1_H\rangle_{11}+|1_H\rangle_{12}+|1_H\rangle_{9}-|1_H\rangle_{10})\\
& +\alpha_2 (|1_H\rangle_{11}-|1_H\rangle_{12})(-|1_V\rangle_{10}+|1_V\rangle_{9}+|1_V\rangle_{12}+|1_V\rangle_{11})\\
&+\alpha_3  (|1_V\rangle_{10}+|1_V\rangle_9)    (|1_H\rangle_{11}+|1_H\rangle_{12}+|1_H\rangle_{9}-|1_H\rangle_{10})\\
& +\alpha_4 (|1_V\rangle_{10}+|1_V\rangle_9)   (-|1_V\rangle_{10}+|1_V\rangle_{9}+|1_V\rangle_{12}+|1_V\rangle_{11})).
\end{split}
\end{eqnarray}

Eq. (\ref{eq21}) indicates that the two-qubit partial-swap operation (i.e., exchanges the information of the two photons, conditional on the first photon being $H$-polarized) is completed when a coincidence is observed  between modes 9 and 11 (10 and 12).   Table \ref{table3}  lists the photon count rates in modes 9 and 11 (10 and 12) for computing basis inputs.

\begin{table}[htb]
\centering \caption{Coincident expectation values calculated for the four logic basis inputs. }
\begin{tabular}{cccccccccccccccc
\toprule
 & $\langle n_{|1_H\rangle_9}n_{|1_H\rangle_{11}}\rangle$ & $\langle n_{|1_H\rangle_9}n_{|1_V\rangle_{11}}\rangle$& $\langle n_{|1_V\rangle_9}n_{|1_H\rangle_{11}}\rangle$     & $\langle n_{|1_V\rangle_9}n_{|1_V\rangle_{11}}\rangle$\\

\cline{2-5}

Input  & $\langle n_{|1_H\rangle_{10}}n_{|1_H\rangle_{12}}\rangle$ & $\langle n_{|1_H\rangle_{10}}n_{|1_V\rangle_{12}}\rangle$ & $\langle n_{|1_V\rangle_{10}}n_{|1_H\rangle_{12}}\rangle$ & $\langle n_{|1_V\rangle_{10}}n_{|1_V\rangle_{12}}\rangle$ \\

\midrule

$|1_H\rangle_{in}|1_H\rangle_{in'}$   & 1/8  &  0  &  0    & 0     \\

$|1_H\rangle_{in}|1_V\rangle_{in'}$   &  0   &  0  &  1/8  & 0     \\

$|1_V\rangle_{in}|1_H\rangle_{in'}$  & 0    &  0  &  1/8  & 0     \\

$|1_V\rangle_{in}|1_V\rangle_{in'}$   & 0    &  0  &  0    & 1/8   \\

\bottomrule
\end{tabular}\label{table3}
\end{table}

\section{Discussion and Conclusion}\label{sec4}

In this paper, we have proposed an effective scheme for fusing $|W_n\rangle$ and $|W_m\rangle$ states into a large-size $|W_{n+m-1}\rangle$ state by using a partial-swap gate. We have also designed a scheme for fusing multiple $W$ states of arbitrary size simultaneously (see Fig. \ref{wn}). By exploiting the spatial  degrees of freedom of single-photons introduced by the PBSs, the partial-swap gate was implemented using an optically polarized architecture designed with linear-optical elements.

As shown in Table \ref{table1}, our scheme outperforms  previous ones in fusing two $W$ states of arbitrary size into a large-sized $W$ state. An ancillary photon, which is necessary in the Fredkin- and Toffoli-based schemes  \cite{Bugu,Fu-T} to create  a $|W_{n+m-1}\rangle$ state, is not required in our scheme. Moreover, our scheme minimizes failure outcomes. From Table \ref{table2}, one can see that, if the gate (Fredkin, Toffoli, CNOT, and partial-swap gates) operations are considered, the fail probability  in the presented scheme is lower than that with the Fredkin- and Toffoli-based schemes \cite{Bugu,Yesilyurt}.

Our presented scheme has the further advantage of reducing cost in terms of the number of two-qubit gates. In previous studies \cite{Bugu,Fu-T}, the fusion of two $W$ states required either one Fredkin gate, or one Toffoli and one CNOT gate. Our presented approach requires just one partial-swap gate. Notably, the optimal cost of an unconstructed Toffoli or Fredkin gate is five two-qubit gates \cite{Optimal1,Optimal2}. If we impose a further condition of using only CNOT gates, at least six CNOT gates are required to synthesize a Toffoli and at least eight for a Fredkin gate \cite{Optimal3}. In contrast, the current proposals based on  partial-swap gates surpass the Fredkin-gate scheme \cite{Bugu} and Toffoli-CNOT-scheme \cite{Fu-T}, and also surpass the scheme based on one Toffoli gate and three CNOT gates \cite{Yesilyurt}  (see Table \ref{table1} and Table \ref{table2}).

Another important advantage of the our scheme is its increased success probability. It is known that entangling quantum gates can be implemented only probabilistically using linear-optical elements. With a polynomial quantum resource, a linear-optical CNOT gate can be implemented  with a maximal success probability of 3/4 \cite{KLM}, and a post-selected CNOT gate with a success probability of 1/9 \cite{1/9}. The most efficient scheme for a CNOT gate with a success probability of 1/4  is achieved with the help of a maximally entangled photon pair  \cite{1/41,1/42}.  Moreover, the ideal  success probability of a Toffoli gate is 1/9 under a linear-optics setup \cite{Toffoli}.  At present, the optimal success probability of a linear optical Fredkin gate is 1/64 \cite{Fredkin}. In contrast, the proposed partial-swap gate with a success probability of 1/4 is achievable. To sum up, our partial-swap-based fusion schemes  outperform the Fredkin-based \cite{Bugu} and Toffoli-CNOT-based schemes \cite{Yesilyurt,Fu-T} in term of the cost and success probability.

\section*{Acknowledgment}

The work was supported by the National Natural Science Foundation of China under Grant No. 11604012, and the Fundamental Research Funds for the Central Universities under Grant Nos.  FRF-BR-17-004B and 230201506500024, and a grant from the China Scholarship Council. KLC is supported by the Ministry of Education and the National Reserach Foundation Singapore.

redpajama_set_name: RedPajamaArXiv


text:
The Lost Desire - Some stories are better left incomplete...
He was in a process of decline, the one which felicitates isolation from the world. Call it the stress at job, or the lack of passion which interpreted in every sphere of his life. It had been 3 years to the day they tied the knot, and the morning following that night was something they would never forget, he had made a breakfast for her. In a span of few minutes which had measured few years along, everything seemed complete. Yet, every morning today, all they do, is to execute the mutual exclusiveness of formality over a cup of caffeine, which they had stopped choosing, they were content with whatever being served.
The mornings passed as the dew drops falling off a leaf to which it no more belonged. The afternoons were the time they indulged in their work, evenings were spent in travelling and the nights in depression.
It was a tiring winter day, a season where even the sweat of hard work chills you down with cold. Sitting on the coffee table, waiting for his daily charge of caffeine, he seemed puzzled with thoughts. There, he sees Natasha bringing his coffee, and just like the previous days admires her, looking at her in daze, in an adorable way, just as she approaches him, she is struck with the presence of a wooden plank on the floor, and the absence of the very same thing from her eyes. She tumbles down. Rajat runs towards her witnessing it, and asks her whether she is fine or not. "I cannot walk, my foot hurts", she said. Rajat knew what was to be done, he picker her up and carried her to the room.
He isolated from her, or vice-versa - they could never come to the conclusion. They still loved each other, the things were perfect just like how it were that morning, but something seemed to lack. Both knew the answer, but none of them ever question. It was passion.
There are stages of life when you have to steps which decide you immediate future, and as well as the one which eventually settles down in coming years.
In those 20 seconds of travels, he had a ride which belonged to his past, to his beloved marriage, and the comfort ability which they shared, seemed to return to its not-so frivolous state. The 20 seconds had taught him the value of someone's presence, and her - the value of him. There was a smile, and a blush which rose on each face. He admired her the whole day, taking care of her foot. They had brought back the old touch, touch of love, touch of inspire, a touch which makes them feel loved, a touch with sparks of life. It was a cold night, and a longer one than usual.
The morning was reminisce to the past, which Natasha fondly remembered - "Good Morning", said Rajat, bringing a cup of coffee and French toast to serve with.
Please do not forget to share the story .
Note : This post was written for a competition on my second channel PixelatedCam. You can check it here.
The Lost Desire - Some stories are better left inc...
9th December 2014 - Are you ready?


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text:
Decriminalizing Mental Health
A regional intervention program aims to get individuals with mental health issues the help they need
Baxter Police Chief Jim Exsted visits with Theresa Rardin at the Crow Wing County Jail booking room. Exsted said this regional collaboration provides another tool for law enforcement, including jail staff, when dealing with individuals suffering from mental illness.
For an unprecedented number of individuals booked into jails across the country, mental illness is a significant, yet undetected, culprit. Region 5 is not immune to that statistic.
According to the National Center for Mental Health and Juvenile Justice, 10 times more people with mental health conditions are in correctional settings versus hospitals, and one in five people in jail has a serious mental illness.
A pilot program recently launched in Region 5 – and supported through Sourcewell Innovation Funding – is already making a difference in helping individuals with mental illness through diversion, early connections with resources, and services and developing discharge plans that truly meet their needs.
Tami Lueck, adult services division manager with Crow Wing County Community Services, is leading an endeavor coined the Region 5+ Comprehensive Re-Entry Project. This program's mission is to provide a comprehensive continuum of care to those who come into contact with the law enforcement community. The program will provide early assessment of any mental health or substance use needs for those who enter the jail.
"When a crime has been committed by someone who is mentally ill, they may end up going to jail rather than getting the help and resources they need," Lueck said. "And that's all over our state, not just something we're facing here in our region. Jails are not the appropriate place for people with mental illness."
Based on data provided by Crow Wing County, 36.7 percent of those booked into jail could be eligible for diversion from detention due to mental illness. Additionally noted: discharge planning efforts in the county have shown a reduction in reoffenses. In 2017, 68 percent of those individuals with discharge plans did not return to jail. This is on track with a 68 percent national average for the first year following discharge.
For Lueck, it all boils down to improved care and timely identification of needs, as well as a streamlined approach throughout the region to access crisis mental health services, diversions, and care for those incarcerated.
After receiving $287,000 in Innovation Funding, the Region 5+ Comprehensive Re-Entry Project was launched in June 2018. A collaboration among the counties of Cass, Crow Wing, Morrison, Todd, Wadena and neighboring Aitkin County, this endeavor was modeled after the Yellow Line Project in Blue Earth County. According to YellowLineProject.com, the program is designed to provide an early response to individuals with acute or chronic mental or chemical health problems who have become involved with law enforcement and are not a risk to the community.
The Yellow Line Project enhances the resources and tools available to law enforcement so that residents get the right services at the right time and have strong incentives to participate in those services.
Lueck said this process was eagerly embraced by other counties around the area, from social and community services to law enforcement and mental health providers.
"Our jail staff came forward with their own concerns of not feeling equipped to manage and serve people with mental illness," Lueck explained. "The lack of inpatient mental health beds across the state also puts pressure on emergency departments. People act out behaviorally and end up in jail. And mental health stakeholders in our communities are concerned about this. It's really sad that we've gotten to a place where that's how we serve people with mental health issues."
As part of the Region 5+ Comprehensive Re-Entry Program, social workers are placed in jails to conduct a 20- to 30-minute screening per individual to determine if mental health issues are present. If not done immediately after someone is brought to the jail, assessments are provided within the first 24 hours following incarceration.
If mental health issues are detected, social service workers are able to intervene and help connect the individual to a resource that can treat the root of the issue – whether it's a temporary residential crisis stabilization home, an inpatient facility, or other source of appropriately handling a mental health situation.
Jails are not the appropriate place for people with mental illness.
Tami Lueck, adult services division manager with Crow Wing County Community Services
In some cases, there may not be a diversion but perhaps an early discharge or discharge with a mutually agreed upon plan.
"We had a case where we were able to assess an individual coming into the jail," Lueck said. "We agreed on a discharge plan. They went to stay at a trusted friend's home. The charging officer, the individual, and social services worker were all in agreement that this plan would work and that the individual wouldn't be a risk to the community. The charges were held by the officer, but the agreement stipulated that the charges would be forwarded if the individual didn't comply with the plan."
Another aspect of the initiative is to equip law enforcement with the knowledge and resources they need to deal with mental illness issues on the front end.
"Sometimes, jail personnel or law enforcement just don't know all of the resources available for people with mental health issues," Lueck added. "Officers have felt like they only have three options: detox, which is limited; inpatient hospitalization, which also comes with limited bed resources; or incarceration. By providing this education, it allows officers to do their jobs and we can come in and do the pieces we're good at. It focuses on partnerships and furthering the relationships between social services and law enforcement."
Unfortunately, Lueck suggests, individuals with mental illness oftentimes fall through the cracks.
"Whether it's an intellectual disability, chemical or drug dependency, or a mental health issue – are they really getting the care they need when they have to ride in the back of a squad car during a crisis? What are the odds of asking for help when that happens? We need to work together to decriminalize mental illness."
Baxter Police Chief Jim Exsted said his department was approached with the idea for a mental health initiative in 2017.
"For law enforcement, we saw this diversion program as an opportunity to provide help to individuals by offering resources instead of sending them to jail," Exsted said. "This program has offered another tool for law enforcement in Crow Wing County when they find themselves dealing with an individual who is struggling with a mental health issue."
And while the diversion side of the program hasn't been as large in numbers as anticipated, the impact it has had on those affected has been significant.
"Initially, we estimated as many as 20 to 30 percent of individuals headed to jail could possibly be diverted," Exsted added. "At this time, we are finding that the diversions are much less than that in Crow Wing County, but the diversions that do occur are extremely impactful. Additionally, the program has allowed the social worker embedded in the jail to meet with and offer services to most individuals who are booked into the facility."
Through this process, Lueck said positive relationships have been forged – including between social services staff placed in the jail for assessments and the individuals they are able to serve.
"It's been interesting to see how relationships are being created. That makes such a big difference with this population. And, on the flipside, employees at the jail appreciate having a social worker there to consult with and ask questions of. There are truly many benefits to this initiative."
While Crow Wing County has served as the pilot for this program, neighboring counties are also putting plans in place to follow suit, with each incorporating a design team consisting of, but not limited to, the county attorney, sheriff's office, social services, police chiefs representing the cities in each respective county, and mental health providers to discuss, support, and carry out the process.
"The communities throughout Region 5 have a lot of good mental health support systems," Lueck noted. "Our hope is to connect those with mental illness to the resources and services they need. And, hopefully, through a variety of scenarios, we all learn how to better manage difficult situations. But, with the right strategies in place, we can all work together to improve the likelihood of individuals getting access to the services they need and the support they deserve. And that's the bottom line."


text:
NRDO
The New Journal of Human Rights | RO | EN |
Books and Studies
PhD Theses Gabriel Andreescu Liviu Andreescu Lucian Bojin Măriuca Oana Constantin Cristi Danileț
Abstracts Nr 3, 2007
Corneliu-Liviu Popescu, Access to Constitutional Justice through Administrative Litigation
The Romanian Constitution guarantees the right of access to the Constitutional Court for the purpose of contesting the constitutional validity of a law or of a governmental ordinance, by invoking an exception of unconstitutionality before a judicial court. In the particular case of governmental ordinances, a direct legal action before the judicial courts for administrative litigations has been considered unconstitutional by the Constitutional Court, for the reason that an exception cannot be transformed into a legal action. At the same time, a possible conflict of legal interpretation between the Constitutional Court, the judicial courts for administrative litigations and the regular judicial courts must not deny real and effective access to constitutional justice.
Gabriel Andreescu, From President Basescu's Blunder to the Issue of Discrimination
The article argues that one may not request the prohibition of "different treatments, exclusions, restrictions and preferences" in opinions and statements made in private. As a result, in sanctioning president Basescu, the CNCD overreached. Other arguments concern the error in introducing Section V in the Ordinance no. 137/2000, which inadequately identifies the value of personal dignity as a right. The consequence of this mistaken identification was the enforcement of the law in question in the absence of adequate means of ensuring the principles of clarity, proportionality and predictability which remain fundamental to any legal norm. The repeal of this section of the Ordinance would enable the CNCD to stress acts of discrimination per se, as well as those policies which may diminish the violently exclusivist and offensive character of public language. As for the incitement to racial and xenophobic hatred, this is already the province of criminal law.
Radu Chiriţă, The Independence and Fairness of Magistrates, or Types of Neutrality of the Judicial Power (II)
The second aspect of magistrate neutrality is fairness. The European understanding of fairness involves both a subjective dimension, which prohibits magistrates' prejudice, and a functional dimension, which prohibits magistrates to rule on issues that were previously ruled upon on a different occasion. As such, ensuring magistrate neutrality at the functional level means little beyond a prohibition of the accretion of a magistrates' decisions for one single case, whether that sole case is the subject of one procedure or more. The final part of the study dwells on the analysis of Romanian jurisprudence in the field, which remains quantitatively limited but adds qualitative information. The final conclusion of the article offers, as a remedy to the prevalent lack of neutrality, an increase in the transparency of the act of justice.
Liviu Andreescu, Religious Education in Some European Countries
In analyzing the education system in several European countries the author shows that: (a) European practices and policies in the field of religious education formally include many or most of the attributes of religious education in Romania; (b) the existing solutions reflect historical arrangements, as well as recent developments which aim at making religious education compatible with general conceptions concerning the education of children; (c) religious education policies in Western Europe have constantly adjusted and have been subordinated to the higher-level principles of freedom of thought, conscience and religion, as well as to the higher interest of the child; (d) while in a sizeable part of Western Europe the dominant trends resulted in bringing religious education closer to the goals and strategies of the non- and/or multi-confessional solution, the Romanian trend has been to give confessional education an increasingly parochial dimension. This is one of the reasons that explain why the system of confessional education in this country is still quite prone to abuse.
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Ritesh Batra
I always cast the right people: Ritesh Batra
Filmmaker Ritesh Batra on casting the right people, setting a budget that can be recovered and whether his films are for a niche audience.
Sanya did a wonderful job, says Ritesh Batra
The film sees Nawazuddin and Sanya sharing the screen for the first time.
Out-of-the-box, into the soul
Ritesh was in the company of legends Redford and Fonda, for his latest film Our Souls At Night that is getting acclaim from all over the world.
Sanya Malhotra teams up with Nawazuddin Siddiqui and Ritesh Batra
Ritesh Batra will now direct Sanya in a film that is set in Mumbai.
Jane and Robert are generous people: Ritesh Batra
The teaser trailer, which is just out, shows the two actors driving together, darting loving glances at each other.
The Sense of an Ending movie review: The past is not of your choosing...
It is the story of Tony Webster, and he makes an attempt to share it with us.
20 May 2017 2:18 AM
Where's The Lunchbox follow-up?
Where is the eagerly awaited follow-up film to Ritesh Batra's The Lunchbox?
I'm in no hurry to tell stories, says Ritesh Batra
Ritesh Batra talks to us about the film, his creative process and more.
Filmmaker Ritesh Batra on books and films, his new movie The Sense of An Ending, and what's to come next.
Nawazuddin Siddiqui to play lead in Ritesh Batra's next
It's an intense subject and is completely different from The Lunchbox, says Nawaz.
I would love to work with Ranbir Kapoor, says Ritesh Batra
In an interview, he speaks about wanting to work with the stars, and his upcoming Hollywood movies.
Ritesh Batra shoots with Jane Fonda and Robert Redford
It's a story set in Colorado about two ageing people, who find happiness together. It's a highly regarded novel.


text:
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Q: Evaluating $\int_0^{\infty} \frac{\sin x}{x} dx$ with Fubini theorem. I have to calculate $\int_0^{\infty} \frac{\sin x}{x} dx$ using Fubini theorem. I tried to find some integrals with property that $\int_x^{\infty} F(t) dt = \frac{1}{x}$, but I cant find anything else but $F(t) = -\frac{1}{x^2}$ and unfortunetely I can't use this.
If I choose $F(t) = -\frac{1}{x}$, then I have:
$\displaystyle \int_0^{\infty} \frac{\sin x}{x} dx = -\int_0^{\infty} \sin x \int_{x}^{\infty} \frac{1}{t^2} dt$,
but I don't know what next

A: The expression $\int_0^\infty \frac{\sin x}{x} dx$ is an abuse of notation, the precise meaning of this expression should be:
$$\lim_{t \to \infty} \int_0^t \frac{\sin x}{x} dx = \frac{\pi}{2} \tag{1}$$
since in fact $x^{-1} \sin x$ is not Lebesgue integrable over $(0, +\infty)$, because its positive and negative parts integrate to $\infty$.
To show $(1)$ using the Fubini's theorem, see, for example, Example $18.4$ of Probability and Measure ($3$rd edition) by Patrick Billingsley.

A: Integrating by parts twice, we get
$$
\begin{align}
&\int_0^L\sin(x)\,e^{-ax}\,\mathrm{d}x\tag{0}\\
&=-\int_0^L e^{-ax}\,\mathrm{d}\cos(x)\tag{1}\\
&=1-e^{-aL}\cos(L)-a\int_0^L\cos(x)\,e^{-ax}\,\mathrm{d}x\tag{2}\\
&=1-e^{-aL}\cos(L)-a\int_0^L e^{-ax}\,\mathrm{d}\sin(x)\tag{3}\\
&=1-e^{-aL}(\cos(L)+a\sin(L))-a^2\int_0^L\sin(x)\,e^{-ax}\,\mathrm{d}x\tag{4}\\
&=\frac{1-e^{-aL}(\cos(L)+a\sin(L))}{1+a^2}\tag{5}
\end{align}
$$
Explanation:
$(1)$: prepare to integrate by parts; $u=e^{-ax}$ and $v=\cos(x)$
$(2)$: integrate by parts
$(3)$: prepare to integrate by parts; $u=e^{-ax}$ and $v=\sin(x)$
$(4)$: integrate by parts
$(5)$: add $\frac{a^2}{1+a^2}$ times $(0)$ to $\frac1{1+a^2}$ times $(4)$
Now we can use Fubini
$$
\begin{align}
\int_0^L\frac{\sin(x)}x\,\mathrm{d}x
&=\int_0^L\sin(x)\int_0^\infty e^{-ax}\,\mathrm{d}a\,\mathrm{d}x\tag{6}\\
&=\int_0^\infty\int_0^L\sin(x)\,e^{-ax}\,\mathrm{d}x\,\mathrm{d}a\tag{7}\\
&=\int_0^\infty\frac{1-e^{-aL}(\cos(L)+a\sin(L))}{1+a^2}\,\mathrm{d}a\tag{8}\\[4pt]
&=\frac\pi2-\int_0^\infty\frac{L\cos(L)+a\sin(L)}{L^2+a^2}e^{-a}\,\mathrm{d}a\tag{9}
\end{align}
$$
Explanation:
$(6)$: $\int_0^\infty e^{-ax}\,\mathrm{d}a=\frac1x$
$(7)$: Fubini
$(8)$: apply $(5)$
$(9)$: arctangent integral and substitute $a\mapsto\frac aL$
Then, by Dominated Convergence, we have that
$$
\begin{align}
\lim_{L\to\infty}\int_0^\infty\left|\frac{L\cos(L)+a\sin(L)}{L^2+a^2}\right|\,e^{-a}\,\mathrm{d}a
&\le\lim_{L\to\infty}\int_0^\infty\frac{L+a}{L^2+a^2}\,e^{-a}\,\mathrm{d}a\\[4pt]
&=0\tag{10}
\end{align}
$$
Therefore, combining $(9)$ and $(10)$, we get
$$
\bbox[5px,border:2px solid #C0A000]{\lim_{L\to\infty}\int_0^L\frac{\sin(x)}x\,\mathrm{d}x=\frac\pi2}\tag{11}
$$

A: $$\int_0^\infty dx \,\frac{\sin x}{x} = \int_0^\infty dx\, \sin x \int_0^\infty dt\, e^{-tx}$$

redpajama_set_name: RedPajamaStackExchange


text:
Tips for Preventing Common Ski and Snowboard Injuries
Stacy McCooey of MountainTop Physical Therapy offers insight into winter's on-mountain injuries and how to best avoid them.
By Michaela Wagner November 20, 2018
Doing just a few targeted exercises ahead of your time on the mountain can greatly reduce your likelihood of sustaining ski and snowboard injuries.
Image: Stacy McCooey
It's probably not the first thing to cross your mind as you strap in for a day on the mountain, but you know skiing and snowboarding are dangerous sports. From minor bumps and bruises to broken bones, injuries are just part of the territory. That said, there are ways to reduce your likelihood of sustaining an injury and minimizing the amount of time you're sidelined in the event you do.
When she's not at work, McCooey takes advantage of Park City via downhill, snowboard, telemark, nordic, touring, fat tire biking, and an occasional snowshoe.
According to Stacy McCooey, an avid outdoors-woman and physical therapist with more than a decade of experience treating ski and snowboard injuries, the winter's most common casualties involve the knees (ACLs) and shoulders, with several spinal (neck and low back) injuries as well. Recovery time, of course, varies from person to person and depends on the severity. "A lot of people can feel better within six weeks, but if the injury requires surgery, return to the sport is typically six months," says McCooey. "As physical therapists we offer evaluation, diagnosis, and treatment. Treatment can range from acute (immediately after the injury) to our Transitional Rehab program which trains people at a high level despite a past or present injury. Physical therapy includes an emphasis on manual (hands-on) therapy and therapeutic exercises, from aquatic therapy and Pilates to dry needling, taping, and so on." Since physical therapists work to optimize the joints and range of motion, this is typically the best route to take if you want a quick return to fitness.
Of course, avoiding injury altogether is preferable. The good news is most injuries can be prevented with simple exercises or minimizing the amount of time you spend walking in ski boots. Knee problems, for instance, can be mitigated by strengthening the hamstrings and hips while shoulder injuries can be offset by working on the rotator cuffs. "I think dry-land training is so important in injury prevention and now is the perfect time to do it," says McCooey. "It depends on your sport and body type, but often we develop muscle imbalances from our activities and daily habits. The general theme is to lengthen what is too short and strengthen what is too long. It is all about creating a balance that allows your joints, muscles, tendons and nerves to function optimally. Balance is crucial within the demands of your sport/desired activity." While it usually takes around six weeks to see meaningful muscle growth from exercise programs, people can begin to gain strength and improve neuro-muscular connections within the first couple of weeks. Although there are dozens of individual exercises, from lunges and squats to hip lifts and everything in between, one of McCooey's favorites is the clamshell (check out the video below).
So what about stretching? Apparently, the jury is still out on the benefits of static position stretching. Instead, McCooey recommends warming the muscles up with some dynamic movement, taking it easy on the first couple of runs, and tuning into what's happening with your body. After a day on the slopes, many of us head straight to the hot tub for a long soak, but it may not be for everyone. "For cooling down, you can try some gentle stretches or other forms of recovery," says McCooey. "A hot tub can feel great and loosen up stiff joints, but it may also increase inflammation. Personally, I feel great jumping in a snow bank after a hard workout! Everyone's body is different so it's important to educate yourself on your own responses and sometimes all you have is trial and error."
Anyone who's wished they too could tumble sans pain into the ridiculous shapes young children do while skiing and snowboarding, also knows injury can become more prevalent as we get older. "Nutrition, genetics, and body type all come into play, but in general, as we age, our bodies become less pliable and we lose muscle mass," says McCooey. "This increases the demand on a maintenance or 'TLC' routine we likely could get by without in years past. The good news is that the effects of aging can largely be mitigated by catching things early, before they turn in to an actual injury." Adding variety to your routine is one of the best ways to do this. Since most of us spend a lot of time sitting, with our legs bent at 90 degrees, and facing forward, any movement that switches up these day-to-day patterns can be helpful, whether it's moving from side to side or getting down into the "third-world squat". McCooey also suggests getting over the 'one final run' syndrome. "Injuries usually happen when we're not feeling one hundred percent and decide to take that last run we're not mentally or physically prepared for," says McCooey. "The most important advice to avoid injury is to always listen to and respect your pain."
Need some more ideas for training? Check out these simple, but effective exercises.
Skiing, Snowboarding, Fitness


text:
2019 Davida Teller Award – Barbara Dosher
The Vision Sciences Society is honored to present Dr. Barbara Dosher with the 2019 Davida Teller Award
VSS established the Davida Teller Award in 2013. Davida was an exceptional scientist, mentor and colleague, who for many years led the field of visual development. The award is therefore given to an outstanding female vision scientist in recognition of her exceptional, lasting contributions to the field of vision science.
Barbara Dosher
Distinguished Professor, University of California, Irvine
Barbara Dosher is a researcher in the areas of visual attention and learning. She received her PhD in 1977 from the University of Oregon and served on the faculty at Columbia University (1977 – 1992) and the University of California, Irvine (1992 – present). Her early career investigated temporal properties of retrieval from long-term and working memory, and priming using pioneering speed-accuracy tradeoff methods. She then transitioned to work largely in vision, bringing some of the concepts of cue combination in memory to initiate work on combining cues in visual perception. This was followed by work to develop observer models using external noise methods that went on to be the basis for proposing that changing templates, stimulus amplification, and noise filtering were the primary functions of attention. This and similar work then constrained and motivated new generative network models of visual perceptual learning that have been used to understand the roles of feedback in unsupervised and supervised learning, the induction of bias in perception, and the central contributions of reweighting evidence to a decision in visual learning.
Barbara Dosher is an elected member of the Society for Experimental Psychologists and the National Academy of Sciences, and is a recipient of the Howard Crosby Warren Medal (2013) and the Atkinson Prize (2018).
Learning and Attention in Visual Perception
Dr. Dosher will speak during the Awards session
Monday, May 20, 2019, 12:30 – 1:45 pm, Talk Room 1-2.
Visual perception functions in the context of a dynamic system that is affected by experience and by top-down goals and strategies. Both learning and attention can improve perception that is limited by the noisiness of internal visual processes and noise in the environment. This brief talk will illustrate several examples of how learning and attention can improve how well we see by amplifying relevant stimuli while filtering others—and how important it is to model the coding or transformation of early features in the development of truly generative quantitative models of perceptual performance.
2020 Davida Teller Award - Marlene Behrmann
2018 Davida Teller Award - Nancy Kanwisher
2017 Davida Teller Award - Mary Hayhoe
2016 Davida Teller Award - Janette Atkinson
2015 Davida Teller Award - Suzanne McKee
2014 Davida Teller Award - Mary C. Potter
2013 Davida Teller Award - Eileen Kowler


text:
Stephen O. "Steve" Plunkett
Fifth Street Towers, 100 South 5th Street, Suite 1500 Minneapolis, Minnesota 55402-1254
splunkett@bassford.com
Firm: Bassford Remele
Contact this lawyer
Bassford Remele
Steve Plunkett concentrates his practice in health care and sexual misconduct defense, bringing nearly 30 years of experience to his role as litigator and counsel.
Mr. Plunkett has defended health care and other clients in hundreds of cases involving bodily injury or the death of residents in group homes and assisted living or skilled nursing facilities. His health care team obtained a defense verdict in 2017 in a significant pressure wound injury case. Mr. Plunkett also represents corporations sued for their employees' sexual misconduct. Recently, he obtained a favorable resolution of several high-profile cases involving former high school students' sexual abuse claims.
Mr. Plunkett is Chair of the Defense Research Institute's Law Institute, where he oversees national seminars on health care law topics including long-term care, medical liability, and other related topics.
Mr. Plunkett is a member of Bassford Remele's Compensation Committee and Chair of its Strategic Planning Committee.
Personal Injury Litigation - Defendants
Professional Malpractice Law - Defendants
United States Court of Appeals for the Tenth Circuit
U.S. District Court for the District of Minnesota
United States Court of Appeals for the Eighth Circuit
Professional Malpractice Law - Defendants, Minneapolis (2023)
Organizations & Affiliations
Defense Research Institute
Chair, Law Institute
University of Minnesota - Minneapolis, J.D.
University of Minnesota - Twin Cities, B.A., Phi Beta Kappa
Fifth Street Towers, 100 South 5th Street, Suite 1500
Minneapolis, Minnesota 55402-1254
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The seventh release on Cure Music comes from Girada Unlimited, featuring two reworks of previously released and very rare tracks.
"Zapatac," the A1, has proven especially popular with Ricardo Villalobos, becoming one of the staples in his recent sets and included in his recent BBC Radio 1 Essential Mix. It is a rework of Velodrome's "Capitaz," released in 1988 as part of the На Велодроме 141 EP via Animalized.
"It took us eight months to get hold of the Velodome guys, namely Krishna Goineau and Jordi Guber," Momo Trosman, label head of Cure recalls. "First we tried contact a label owner that had a connection with Jordi but didn't want to provide us the contact. After that, we did some research and wrote to all the labels that had released something from Liaisons Dangereuses trying to contact Krishna. It was a nightmare, no one answered us and we sent over 15 emails." Then, after a few months, Trosman received a cellphone number as a reply of one of the emails and touched based with Krishna who said: "I love the idea of doing this together and why not to release more old unreleased stuff in the future." After two weeks, Trosman then made contact with Jordi who said that they used to "hate hi-hats" and that "if someone had told him 20 years ago that there would be a Velodrome edit with hi-hats that he would never have believed it." But now he "loves it," we're told.
The identity of Girada Unlimited remains unconfirmed, but it is an alias previously used by Julian Perez and the name of his label. We're told that this is just one example of many older tunes he or she has edited into some a little more playable.
Details of "Reserval," the second track, remain unknown barring that it's another edit or a rare old record.
Where's Daff? will land next month, with a snippet of "Zapatac" available below.