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Cardi B cancels performances to recover from plastic surgery
Cardi B cancels performances to recover from plastic surgery after strict doctors orders. The singer was "overzealous in getting back to work".
Offset has revealed that he is taking things very slowly with Cardi B
Cardi B will be spending the holidays with Offset despite cheating
The model that drove a wedge between Cardi B and Offset has spoken out
Cardi B shows off her post-pregnancy body at New York Fashion Week
Offset gets his daughter Kulture's name tattooed across his face
Offset recently had his youngest daughter's name tattooed on his face. The rapper had daughter Kulture Kiari Cephus with Cardi B a few months ago.
Cardi B shows off post-baby body and new matching Lamborghini set with Offset
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Offset is home after being arrested in Georgia: he is facing four charges
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Affirmation: Love illuminates the core of my Being… birthing the shadows into the light.
Increases our ability to feel the love that exists all around us…more able to love ourselves, family, friends & life. Self love is the core of all our experiences. We all need to learn to love ourselves, and our many aspects or facets more deeply. The vibration of love is the bedrock, the foundation from which all else flows.
Choose this if you are feeling abandoned, rejected or if you're having challenges finding things to love within yourself. When love is not being felt, fear is present so choose this to move beyond the fear & into love.
Self love, love for others, love for Source, respect, attraction, admiration.
Fear, hatred, self- loathing, rejection, abandonment, criticism, judgment, separation, not belonging to a group or being a part of things.
Set your intention to RESONATE LOVE and take 7 drops morning & night to Raise your Vibration.
66% Purified Water, 34% Vodka (12.75% alcohol) Vibrations of colour, light & sound resonating Pure Consciousness of LOVE.


YEREVAN, SEPTEMBER 8, ARMENPRESS. Former Prime Minister of Armenia Hovik Abrahamyan is charged with part 1 of Article 309 of the criminal code of Armenia (abuse of power) and Article 310 ) Illegal participation in entrepreneurial activity), ARMENPRESS was informed from the press service of the Special Investigation Service. Written obligation not to leave the place of residence has been chosen as a preventive measure for him.
Earlier, Hovik Abrahamyan informed about accusation against him. He wrote on his Facebook page that on September 4 the Special investigation Service sent him a notification for interrogation as a witness, afterwards charges were pressed.
The investigation into the criminal case revealed that "Avazahatik" company, established in 2000 in Ararat Province, was engaged in mining. But in 2008 high ranking officials created artificial obstacles and demanded 60% shares of the company.
The founder of "Avazahatik" company and other witnesses have indicated the names of Hovik and Jonik Abrahamyans and Alik Sargsyan in their testimonies among the individuals linked with power abuse.


text:
package com.rockerhieu.emojicon;

import java.util.Arrays;
import android.app.Activity;
import android.os.Bundle;
import android.support.v4.app.Fragment;
import android.view.LayoutInflater;
import android.view.View;
import android.view.ViewGroup;
import android.widget.AdapterView;
import android.widget.GridView;
import com.rockerhieu.emojicon.emoji.Emojicon;
import com.rockerhieu.emojicon.emoji.People;

/**
 * @author Hieu Rocker (rockerhieu@gmail.com)
 */
public class EmojiconGridFragment extends Fragment implements AdapterView.OnItemClickListener {
    private OnEmojiconClickedListener mOnEmojiconClickedListener;
    private EmojiconRecents mRecents;
    private Emojicon[] mData;
    private boolean mUseSystemDefault = false;

    private static final String USE_SYSTEM_DEFAULT_KEY = "useSystemDefaults";

    protected static EmojiconGridFragment newInstance(Emojicon[] emojicons, EmojiconRecents recents) {
        return newInstance(emojicons, recents, false);
    }

    protected static EmojiconGridFragment newInstance(Emojicon[] emojicons, EmojiconRecents recents, boolean useSystemDefault) {
        EmojiconGridFragment emojiGridFragment = new EmojiconGridFragment();
        Bundle args = new Bundle();
        args.putSerializable("emojicons", emojicons);
        args.putBoolean(USE_SYSTEM_DEFAULT_KEY, useSystemDefault);
        emojiGridFragment.setArguments(args);
        emojiGridFragment.setRecents(recents);
        return emojiGridFragment;
    }

    @Override
    public View onCreateView(LayoutInflater inflater, ViewGroup container, Bundle savedInstanceState) {
        return inflater.inflate(R.layout.emojicon_grid, container, false);
    }

    @Override
    public void onViewCreated(View view, Bundle savedInstanceState) {
        GridView gridView = (GridView) view.findViewById(R.id.Emoji_GridView);
        Bundle bundle = getArguments();
        if (bundle == null) {
            mData = People.DATA;
            mUseSystemDefault = false;
        } else {
            Object[] o = (Object[]) getArguments().getSerializable("emojicons");
            mData = Arrays.asList(o).toArray(new Emojicon[o.length]);
            mUseSystemDefault = bundle.getBoolean(USE_SYSTEM_DEFAULT_KEY);
        }
        gridView.setAdapter(new EmojiAdapter(view.getContext(), mData, mUseSystemDefault));
        gridView.setOnItemClickListener(this);
    }

    @Override
    public void onSaveInstanceState(Bundle outState) {
        super.onSaveInstanceState(outState);
        outState.putSerializable("emojicons", mData);
    }

    @Override
    public void onAttach(Activity activity) {
        super.onAttach(activity);
        if (activity instanceof OnEmojiconClickedListener) {
            mOnEmojiconClickedListener = (OnEmojiconClickedListener) activity;
        } else if (getParentFragment() instanceof OnEmojiconClickedListener) {
            mOnEmojiconClickedListener = (OnEmojiconClickedListener) getParentFragment();
        } else {
            throw new IllegalArgumentException(activity + " must implement interface " + OnEmojiconClickedListener.class.getSimpleName());
        }
    }

    @Override
    public void onDetach() {
        mOnEmojiconClickedListener = null;
        super.onDetach();
    }

    @Override
    public void onItemClick(AdapterView<?> parent, View view, int position, long id) {
        if (mOnEmojiconClickedListener != null) {
            mOnEmojiconClickedListener.onEmojiconClicked((Emojicon) parent.getItemAtPosition(position));
        }
        if (mRecents != null) {
            mRecents.addRecentEmoji(view.getContext(), ((Emojicon) parent
                .getItemAtPosition(position)));
        }
    }

    private void setRecents(EmojiconRecents recents) {
        mRecents = recents;
    }

    public interface OnEmojiconClickedListener {
        void onEmojiconClicked(Emojicon emojicon);
    }
}

redpajama_set_name: RedPajamaGithub


text:
The ERN+ Project
What is resettlement?
Resettlement as a life saving tool
Videos - Emergency & Urgent Resettlement
The resettlement process
Identification phase
Selection phase
Pre-departure assistance phase
Travel phase
Reception phase
Integration phase
SHARE Network
Pre-Arrival Planning
Settlement & Early Integration
National & Local Partnerships
Emerging Resettlement Countries
VOICES OF PREVIOUSLY RESETTLED REFUGEES...
SHARE Publications & Resources
Resettlement in Europe
Current European Response
EU funding for resettlement
The role of the European Asylum Support Office (EASO)
EU-FRANK
LINK-IT project
Complementary Pathways
Community-based Private Sponsorship
Other forms of Humanitarian Admission
ERN+ Publications
ERN+ Webinars
ERN+ Webinar on Humanitarian Admission in Europe
ERN+ Webinar on Higher Education Opportunities for Refugee Students
ERN+ Webinar on Private Sponsorship of Refugees in Europe
ERN+ Conference on Complementary Pathways
ERN+ Churches Conference
ERN+ Resettlement Stakeholder Exchange
ERN+ Round Tables on Complementary Pathways
Find Tools & Resources
Search Practices
Refugee testimonies
Login Register Forgot password?
Burmese refugees in Thailand & Malaysia
Congolese (DRC) refugees
Somali refugees in Kenya & Ethiopia
Eritrean refugees in Eastern Sudan
The Colombian refugee situation
Afghan refugees in Iran & Pakistan
Bhutanese refugees in Nepal
Iranian & Iraqi refugees in Turkey
Iraqi refugees in Jordan, Lebanon & Syria
The Syrian refugee situation
Source: ICMC Europe, Welcome to Europe! A comprehensive guide to resettlement, 2013
Prolonged conflict in Burma (Myanmar) has led to one of the most protracted refugee situations in Asia. For over 50 years, the Burmese military regime has persecuted many of the country's numerous ethnic and minority groups, many of whom have sought greater autonomy from the Burmese state. Burma's human rights situation remains poor, despite some actions by the government toward reform.
Burmese refugees in Malaysia
As of January 2014, 92,263 Burmese refugees were registered in Malaysia. The Burmese refugee population in Malaysia is entirely urban, with most living in or around major cities. This population is made up of ethnic Burmese minorities who fled persecution by the former military regime, mainly the Chin, Karen and Mon groups. The Burmese refugee population in Malaysia also includes a large group of Rohingya, a Muslim minority from Burma's northern Rakhine State that suffers routine discrimination and abuse by the Burmese government. Peace negotiations with armed ethnic groups are ongoing, and prospects for voluntary return are therefore expected to improve in 2013-14. However, continuous persecution and instability in some parts of Burma mean voluntary repatriation is still not a realistic prospect for the majority of Burmese refugees in Malaysia.
Prospects for local integration are also extremely limited. Malaysia is not a signatory to the 1951 Convention or its 1967 Protocol, and has no national asylum legal framework or system (RSD is instead conducted by UNHCR). Urban environments can in some cases offer more opportunities for self reliance and better prospects for integration. However, the 1963 Malaysian Immigration Act does not distinguish between refugees and undocumented migrants, and without a protected legal status refugees are at constant risk of arrest, detention and deportation. Refugees are unable to work legally, send their children to school, or access healthcare or social services.
For 2014, UNHCR plans to submit 14,150 Burmese refugees for resettlement from Malaysia, contributing to making it the country with the highest number of resettlement submissions worldwide planned for 2014. Total resettlement needs are 123,760 Burmese refugees. In addition to annual intakes by Canada, Australia, New Zealand and the US have multi-year resettlement commitments with regard to this population.
European countries including Czech Republic, Denmark, Norway and Sweden have resettled Burmese refugees. Identification of resettlement needs is challenging due to the urban context, although UNHCR accepts referrals for resettlement assessment from refugee communities and NGOs, particularly those involved in health and community services in urban settings.
Certain NGOs have pointed out that resettlement from Malaysia should be used more strategically and be used to promote an adequate protection system in Malaysia, where most refugees have remained in this protracted situation for decades without a durable solution in sight.
Burmese refugees in Thailand
Since their arrival in Thailand in the 1980s, Burmese refugees have been confined to nine closed camps – known as 'temporary shelters' - along the Thai-Burma border. Access to these camps is regulated by the Thai government. As of January 2014, 77,913 Burmese refugees were registered as having been admitted to the nine camps. Since 2006, the registration and admission system in the camps has not been fully functional, and approximately 46,000 camp residents are estimated to be unregistered. Unregistered camp residents are ineligible for resettlement. UNHCR conducts RSD for asylum seekers living in Bangkok except for Burmese refugees who are required by the government to report to the camps on the border.
Most camp residents are ethnic Karen who fled conflict with the military regime in Burma. Following national elections in Burma in November 2010, new clashes between armed ethnically affiliated groups and the Burmese army erupted along the Thai-Burma border, leading to the rapid arrival of a further 16,000-18,000 refugees from Burma. While recent ceasefire agreements between ethnic armed groups and the Burmese government have presented some limited possibilities for a resolution to these conflicts, it is not clear when - or even if - the situation will improve. Many Karen refugees are subsequently reluctant to take up voluntary repatriation at the current time, and it therefore remains limited as a durable solution in this context.
Thailand is not a signatory to the 1951 Convention and has no national legislation governing the treatment of refugees. Burmese nationals, found living outside of the camps, are subject to arrest, detention and deportation. The basic rights of refugees in Thailand are severely limited - they have no access to medical services and they do not have the right to work – meaning local integration is impossible. To date, resettlement has been the only durable solution that offers adequate protection for Burmese refugees in Thailand.
Resettlement began in 2005 and has since provided a durable solution for more than 80,000 Burmese refugees in Thailand. UNHCR has projected a total resettlement need for Burmese refugees in Thailand of 4,000 persons, and plans to submit 3,500 refugees for resettlement in 2014. Although resettlement from Thailand has been conducted for over seven years, it has not led to an improvement in the protection climate in Thailand. UNHCR is in the process of phasing out resettlement and no longer lists it as a priority for 2014.
Photo: Nam DarBu, Burmese (Karen) refugee living in Kuala Lumpar. ©Andrew McConnel/Panos Pictures/The IRC
Partnerships for refugee inclusion in local communities across Europe
Subscribe to receive updates, newsletters, events invitations and best practice publications from the European Resettlement Network and the SHARE Network in the areas of integration, resettlement and complementary pathways of admission to access protection in Europe.
© 2007 - European Resettlement Network
Site by Crossmark
This website is partly funded by the European Union

redpajama_set_name: RedPajamaCommonCrawl


Thirteen are arrested; Bilal Kayed is still being held after completing a 14-year sentence for offenses during the second intifada.
Right-wing extremists threw stones on Tuesday at demonstrators protesting the detention conditions of a Palestinian administrative detainee. Thirteen people were arrested, most of them for throwing stones.


text:
H.R.4176 - Prevention of Unsafe Licensing Act110th Congress (2007-2008)
Rep. King, Peter T. [R-NY-3] (Introduced 11/14/2007)
House - Transportation and Infrastructure; Oversight and Government Reform
House - 11/15/2007 Referred to the Subcommittee on Highways and Transit. (All Actions)
Transportation and Public Works
Cosponsors: H.R.4176 — 110th Congress (2007-2008)All Information (Except Text)
Sponsor: Rep. King, Peter T. [R-NY-3] | Cosponsor statistics: 170 current - includes 156 original
* = Original cosponsor
Sort by Sort by: First to LastLast to FirstAlphabetical - By NameAlphabetical - By PartyAlphabetical - By State
Date Cosponsored
Rep. Sessions, Pete [R-TX-32]* 11/14/2007
Rep. Boehner, John A. [R-OH-8]* 11/14/2007
Rep. Blunt, Roy [R-MO-7]* 11/14/2007
Rep. Putnam, Adam H. [R-FL-12]* 11/14/2007
Rep. Smith, Lamar [R-TX-21]* 11/14/2007
Rep. Kuhl, John R. "Randy", Jr. [R-NY-29]* 11/14/2007
Rep. Reynolds, Thomas M. [R-NY-26]* 11/14/2007
Rep. McHugh, John M. [R-NY-23]* 11/14/2007
Rep. Fossella, Vito [R-NY-13]* 11/14/2007
Rep. Gillibrand, Kirsten E. [D-NY-20]* 11/14/2007
Rep. Miller, Candice S. [R-MI-10]* 11/14/2007
Rep. Burton, Dan [R-IN-5]* 11/14/2007
Rep. Tancredo, Thomas G. [R-CO-6]* 11/14/2007
Rep. Myrick, Sue Wilkins [R-NC-9]* 11/14/2007
Rep. Baker, Richard H. [R-LA-6]* 11/14/2007
Rep. Dreier, David [R-CA-26]* 11/14/2007
Rep. Feeney, Tom [R-FL-24]* 11/14/2007
Rep. Davis, David [R-TN-1]* 11/14/2007
Rep. Davis, Tom [R-VA-11]* 11/14/2007
Rep. Boyda, Nancy E. [D-KS-2]* 11/14/2007
Rep. Shays, Christopher [R-CT-4]* 11/14/2007
Rep. Brown, Henry E., Jr. [R-SC-1]* 11/14/2007
Rep. McCotter, Thaddeus G. [R-MI-11]* 11/14/2007
Rep. Emerson, Jo Ann [R-MO-8]* 11/14/2007
Rep. McIntyre, Mike [D-NC-7]* 11/14/2007
Rep. Roskam, Peter J. [R-IL-6]* 11/14/2007
Rep. Chabot, Steve [R-OH-1]* 11/14/2007
Rep. Bilirakis, Gus M. [R-FL-9]* 11/14/2007
Rep. Pence, Mike [R-IN-6]* 11/14/2007
Rep. Culberson, John Abney [R-TX-7]* 11/14/2007
Rep. Poe, Ted [R-TX-2]* 11/14/2007
Rep. Drake, Thelma D. [R-VA-2]* 11/14/2007
Rep. Tiahrt, Todd [R-KS-4]* 11/14/2007
Rep. Gingrey, Phil [R-GA-11]* 11/14/2007
Rep. Deal, Nathan [R-GA-9]* 11/14/2007
Rep. Peterson, John E. [R-PA-5]* 11/14/2007
Rep. Pearce, Stevan [R-NM-2]* 11/14/2007
Rep. Sullivan, John [R-OK-1]* 11/14/2007
Rep. Tiberi, Patrick J. [R-OH-12]* 11/14/2007
Rep. Simpson, Michael K. [R-ID-2]* 11/14/2007
Rep. Royce, Edward R. [R-CA-40]* 11/14/2007
Rep. McCaul, Michael T. [R-TX-10]* 11/14/2007
Rep. Souder, Mark E. [R-IN-3]* 11/14/2007
Rep. Hulshof, Kenny C. [R-MO-9]* 11/14/2007
Rep. King, Steve [R-IA-5]* 11/14/2007
Rep. Marchant, Kenny [R-TX-24]* 11/14/2007
Rep. Ramstad, Jim [R-MN-3]* 11/14/2007
Rep. Akin, W. Todd [R-MO-2]* 11/14/2007
Rep. LoBiondo, Frank A. [R-NJ-2]* 11/14/2007
Rep. Ferguson, Mike [R-NJ-7]* 11/14/2007
Rep. Campbell, John [R-CA-48]* 11/14/2007
Rep. Kline, John [R-MN-2]* 11/14/2007
Rep. Walsh, James T. [R-NY-25]* 11/14/2007
Rep. Keller, Ric [R-FL-8]* 11/14/2007
Rep. Smith, Adrian [R-NE-3]* 11/14/2007
Rep. Dent, Charles W. [R-PA-15]* 11/14/2007
Rep. Coble, Howard [R-NC-6]* 11/14/2007
Rep. Alexander, Rodney [R-LA-5]* 11/14/2007
Rep. Terry, Lee [R-NE-2]* 11/14/2007
Rep. Hall, Ralph M. [R-TX-4]* 11/14/2007
Rep. Bachus, Spencer [R-AL-6]* 11/14/2007
Rep. Rehberg, Dennis R. [R-MT-At Large]* 11/14/2007
Rep. Lucas, Frank D. [R-OK-3]* 11/14/2007
Rep. Calvert, Ken [R-CA-44]* 11/14/2007
Rep. Aderholt, Robert B. [R-AL-4]* 11/14/2007
Rep. Herger, Wally [R-CA-2]* 11/14/2007
Rep. McHenry, Patrick T. [R-NC-10]* 11/14/2007
Rep. Duncan, John J., Jr. [R-TN-2]* 11/14/2007
Rep. Bilbray, Brian P. [R-CA-50]* 11/14/2007
Rep. Reichert, David G. [R-WA-8]* 11/14/2007
Rep. Musgrave, Marilyn N. [R-CO-4]* 11/14/2007
Rep. Lewis, Ron [R-KY-2]* 11/14/2007
Rep. Young, C. W. Bill [R-FL-10]* 11/14/2007
Rep. Hunter, Duncan [R-CA-52]* 11/14/2007
Rep. LaTourette, Steven C. [R-OH-14]* 11/14/2007
Rep. Latham, Tom [R-IA-4]* 11/14/2007
Rep. Doolittle, John T. [R-CA-4]* 11/14/2007
Rep. Gerlach, Jim [R-PA-6]* 11/14/2007
Rep. Hensarling, Jeb [R-TX-5]* 11/14/2007
Rep. Renzi, Rick [R-AZ-1]* 11/14/2007
Rep. Shadegg, John B. [R-AZ-3]* 11/14/2007
Rep. Linder, John [R-GA-7]* 11/14/2007
Rep. Neugebauer, Randy [R-TX-19]* 11/14/2007
Rep. Saxton, Jim [R-NJ-3]* 11/14/2007
Rep. Gohmert, Louie [R-TX-1]* 11/14/2007
Rep. Wolf, Frank R. [R-VA-10]* 11/14/2007
Rep. Goode, Virgil H., Jr. [R-VA-5]* 11/14/2007
Rep. Miller, Jeff [R-FL-1]* 11/14/2007
Rep. Platts, Todd Russell [R-PA-19]* 11/14/2007
Rep. Franks, Trent [R-AZ-2]* 11/14/2007
Rep. Blackburn, Marsha [R-TN-7]* 11/14/2007
Rep. Wicker, Roger F. [R-MS-1]* 11/14/2007
Rep. Gallegly, Elton [R-CA-24]* 11/14/2007
Rep. Broun, Paul C. [R-GA-10]* 11/14/2007
Rep. Brown-Waite, Ginny [R-FL-5]* 11/14/2007
Rep. Cole, Tom [R-OK-4]* 11/14/2007
Rep. Johnson, Sam [R-TX-3]* 11/14/2007
Rep. Burgess, Michael C. [R-TX-26]* 11/14/2007
Rep. Murphy, Tim [R-PA-18]* 11/14/2007
Rep. Wilson, Joe [R-SC-2]* 11/14/2007
Rep. Rogers, Mike J. [R-MI-8]* 11/14/2007
Rep. Barrett, J. Gresham [R-SC-3]* 11/14/2007
Rep. Price, Tom [R-GA-6]* 11/14/2007
Rep. Granger, Kay [R-TX-12]* 11/14/2007
Rep. Fortenberry, Jeff [R-NE-1]* 11/14/2007
Rep. Davis, Geoff [R-KY-4]* 11/14/2007
Rep. Thornberry, Mac [R-TX-13]* 11/14/2007
Rep. Capito, Shelley Moore [R-WV-2]* 11/14/2007
Rep. Buyer, Steve [R-IN-4]* 11/14/2007
Rep. Fallin, Mary [R-OK-5]* 11/14/2007
Rep. Bonner, Jo [R-AL-1]* 11/14/2007
Rep. Bachmann, Michele [R-MN-6]* 11/14/2007
Rep. Forbes, J. Randy [R-VA-4]* 11/14/2007
Rep. Boozman, John [R-AR-3]* 11/14/2007
Rep. Turner, Michael R. [R-OH-3]* 11/14/2007
Rep. Everett, Terry [R-AL-2]* 11/14/2007
Rep. Kingston, Jack [R-GA-1]* 11/14/2007
Rep. Schmidt, Jean [R-OH-2]* 11/14/2007
Rep. Porter, Jon C. [R-NV-3]* 11/14/2007
Rep. Rogers, Harold [R-KY-5]* 11/14/2007
Rep. Barton, Joe [R-TX-6]* 11/14/2007
Rep. Frelinghuysen, Rodney P. [R-NJ-11]* 11/14/2007
Rep. Bono, Mary [R-CA-45]* 11/14/2007
Rep. Young, Don [R-AK-At Large]* 11/14/2007
Rep. Pryce, Deborah [R-OH-15]* 11/14/2007
Rep. Brady, Kevin [R-TX-8]* 11/14/2007
Rep. Westmoreland, Lynn A. [R-GA-3]* 11/14/2007
Rep. English, Phil [R-PA-3]* 11/14/2007
Rep. Rohrabacher, Dana [R-CA-46]* 11/14/2007
Rep. Issa, Darrell E. [R-CA-49]* 11/14/2007
Rep. Graves, Sam [R-MO-6]* 11/14/2007
Rep. Rogers, Mike D. [R-AL-3]* 11/14/2007
Rep. Wamp, Zach [R-TN-3]* 11/14/2007
Rep. Conaway, K. Michael [R-TX-11]* 11/14/2007
Rep. Hayes, Robin [R-NC-8]* 11/14/2007
Rep. Pickering, Charles W. "Chip" [R-MS-3]* 11/14/2007
Rep. McMorris Rodgers, Cathy [R-WA-5]* 11/14/2007
Rep. Weldon, Dave [R-FL-15]* 11/14/2007
Rep. Kirk, Mark Steven [R-IL-10]* 11/14/2007
Rep. McKeon, Howard P. "Buck" [R-CA-25]* 11/14/2007
Rep. Hobson, David L. [R-OH-7]* 11/14/2007
Rep. Hastert, J. Dennis [R-IL-14]* 11/14/2007
Rep. Cubin, Barbara [R-WY-At Large]* 11/14/2007
Rep. McCarthy, Kevin [R-CA-22]* 11/14/2007
Rep. McCrery, Jim [R-LA-4]* 11/14/2007
Rep. Shuster, Bill [R-PA-9]* 11/14/2007
Rep. Lamborn, Doug [R-CO-5]* 11/14/2007
Rep. Johnson, Timothy V. [R-IL-15]* 11/14/2007
Rep. Boustany, Charles W., Jr. [R-LA-7]* 11/14/2007
Rep. Goodlatte, Bob [R-VA-6]* 11/14/2007
Rep. Whitfield, Ed [R-KY-1]* 11/14/2007
Rep. Miller, Gary G. [R-CA-42]* 11/14/2007
Rep. Mica, John L. [R-FL-7]* 11/14/2007
Rep. Moran, Jerry [R-KS-1]* 11/14/2007
Rep. Jordan, Jim [R-OH-4]* 11/14/2007
Rep. Knollenberg, Joe [R-MI-9]* 11/14/2007
Rep. Carter, John R. [R-TX-31] 11/15/2007
Rep. Gilchrest, Wayne T. [R-MD-1] 11/15/2007
Rep. Buchanan, Vern [R-FL-13] 11/15/2007
Rep. Smith, Christopher H. [R-NJ-4] 11/15/2007
Rep. Bartlett, Roscoe G. [R-MD-6] 11/15/2007
Rep. Barrow, John [D-GA-12] 11/15/2007
Rep. Upton, Fred [R-MI-6] 11/15/2007
Rep. Hoekstra, Peter [R-MI-2] 12/04/2007
Rep. Jones, Walter B., Jr. [R-NC-3] 12/04/2007
Rep. Walberg, Timothy [R-MI-7] 12/04/2007
Rep. Lewis, Jerry [R-CA-41] 12/18/2007
Rep. Altmire, Jason [D-PA-4] 01/23/2008
Rep. Latta, Robert E. [R-OH-5] 03/11/2008
Rep. Cantor, Eric [R-VA-7] 03/31/2008
Republican [165]
Cosponsors by U.S. State or Territory
Texas [18]
California [16]
Florida [10]
Ohio [10]
Pennsylvania [8]
Michigan [7]
Virginia [7]
New York [6]
North Carolina [6]
Alabama [5]
Missouri [5]
New Jersey [5]
Illinois [4]
Indiana [4]
Kentucky [4]
Louisiana [4]
Oklahoma [4]
Tennessee [4]
Kansas [3]
Minnesota [3]
Nebraska [3]
South Carolina [3]
Iowa [2]
Maryland [2]
Mississippi [2]
Alaska [1]
Arkansas [1]
Connecticut [1]
Idaho [1]
Montana [1]
New Mexico [1]
West Virginia [1]
Wyoming [1]


Where are you calling from? best essays online 304 Date of Birth N 8 variable R The Recipient's birth date.
I'd like to withdraw $100, please cleocin gel during rotation and review by faculty following completion of the IPPE.


text:
ILO is a United Nations Agency
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Database of national labour, social security and related human rights legislation
NATLEX home
Recent important additions to NATLEX
Iceland (379) > Social security (general standards) (82)
Original name: Lög um félagslega aðstoð nr. 99/2007
Name: Act on Social Assistance, No. 99/2007.
Country: Iceland
Subject(s): Social security (general standards)
Type of legislation: Law, Act
Adopted on: 2007
ISN: ISL-2007-L-82812
Link: https://www.ilo.org/dyn/natlex/natlex4.detail?p_isn=82812&p_lang=en
Bibliography: Legislation on-line Ministry of Welfare, Iceland PDF of Act in English as amended to Act No. 96/2017 (consulted on 2016-05-10)
Legislation on-line Parliament of Iceland - Althingi, Iceland PDF of Act in Icelandic as amended to Act No. 126/2016 (consulted on 2017-05-29)
Abstract/Citation: Social assistance benefits consist of: single parent's allowance, child pension in connection with school studies or vocational training of young people aged 18-20, home-care allowance, spouse's benefit, home-care benefit, death benefit, rehabilitation pension, household supplement, automobile purchase supplements, automobile operation supplements and reimbursements of substantial expenses in connection with medical assistance and medications. Social assistance benefits are paid only to persons who are legally domiciled in Iceland.
Repealed text(s):
1993-12-23 (ISL-1993-L-46317)Act No. 118 of 1993 on social assistance.
Amending text(s):
2016-06-16 (ISL-2016-L-104424)Act on Housing Benefits, No. 75/2016
Implementing text(s):
2009-06-23 (ISL-2009-R-91290)Regulations on the calculation, recalculation and settlement of income-related benefits and contributions No. 598/2009.
Related text(s):
2007-05-11 (ISL-2007-L-91291)Social Security Law No. 100/2007.
1999 (ISL-1999-L-82809)Act on the Affairs of the Elderly, No. 125/1999.
1993-12-23 (ISL-1993-L-46623)Act No. 117 of 1993 on Social Security.


Beauty lies in the eyes of the beholder- Margaret Hungerford. A smile has been said to be one of the most important interactive communication skill of person. The ultimate objective of aesthetics in dentistry is to create a beautiful smile, with teeth of pleasing inherent proportion to one another and a pleasing tooth arrangement in harmony with the gingiva, lips and face of the patient. Patients now demand not only a healthy mouth but also a perfect smile. The smile, which represents the most primitive form and the essence of human communicative ability, appears early in life in young children. Smiles and later facial expressions express transient feelings and emotions. Esthetic Dentistry demands attention to the patient's desires and treatment of patients desires and treatment of patient's individual problems. Goldstein states "Esthetic dentistry is the art of dentistry in its purest form". The purpose is not to sacrifice the function but to use it as a foundation of esthetics. Through technological advances, it is now possible to enhance and strengthen the health and function of a patient's appearance and smile conservatively. The true understanding of all aspects of comprehensive esthetic/cosmetic dentistry and the integration of the philosophical triad of "health, function and beauty" will assist the dentist in providing optimal dental care.


Dear Mary! Another wonderful and informative part of the series that is so near to your heart.
Unfortunately, the heretical idea that Jesus became sinful/a sinner has been around for ever. Here's a link to an article on someone I truly believe to be a false teacher (for many reasons) and who has taught that very same heresy.
Thanks, Mary, and may this post reach, with the Holy Spirit's help and the willingness of people to listen, the minds of those who are trapped in this manmade tradition called Roman Catholicism.
Thank you for your words of encouragement, Valerie, and thank you for the additional information, as well! Thank you especially for your heartfelt prayer for Catholics to become willing to listen. My deepest desire and prayer is for them to see the truth about the Biblical gospel that is revealed in God's Word that gives life, joy, and peace, instead of the fear and uncertainty that comes from the teachings of Catholicism.
God bless you…and your husband and family, dear Sister-in-Christ!
Please note that I do not endorse this link or the one link I've given above, as their theology does NOT reflect and correspond with God's Word in any way whatsoever. I am supplying these links for academic value and input only, so please enter those sites with caution like a true Berean.
The JW say the same thing!!! You just can't understand Scripture without someone in hierarchy explaining it to you. Mormons and SDA also have their prophets to tell you what the Scripture really says. All cults say only their leaders have the true understanding — which is why I consider the RCC a cultic organization.
Just this teaching alone is enough to prove that Romanism is dangerous.
As for the virgin Mary, I've also demonstrated that the RCC Mary is not the Mary of the Bible.
Thanks for your citations proving the RCC teachings are made up out of whole cloth.
Thank you for your comment, Glenn. Yes, I shared that disturbing quote in Part 1 of this series…I found it in the opening pages of my mom and dad's Douay Rheims Bible. it's very sad how Catholics are discouraged from reading the Bible on their own. As I have shared in Part 1 of mt testimony I became a Christian because of the truth that I found as I began to read a Catholic Bible on my own. Just imagine how many more Catholics would come to the knowledge of the true gospel if only they would read it on their own and ask God to show them what the truth really is! That is my prayer…that this series will get Catholics to begin to question what they believe and to seek God for the truth in His Word.
Thank you for sharing the link to your post on Mary…I'll read it when time allows. In Part 2 of 'My Testimony' I shared a LOT of disturbing information concerning who the Mary of Catholicism is, and, Lord willing, I will be sharing some more at some point in this series, as well as some information on the Pope when I get to that part in the Catechism book.
Once again Mary what incredible information. The Lord bless you richly.
Thank you so much for your encouraging comment, Jane. These posts are very important to me because the desire of my heart is for Catholics to realize the truth that can be found in God's Word –the Bible. When someone's eternal destiny is at stake we must do all that we can to point them to Jesus Christ and help them to question what they have been taught and believe to be true.
May the Lord bless you richly, as well, dear Jane!


What makes your app stand out from the competition? Great design? Good user targeting? Most of these factors contribute to your app's success. When looking at apps created by the industry giants, most of them have a few things in common.
For instance, these popular apps have a great user-friendly appearance and feel. But what does a good app cost really mean? Let's find out by defining how much your app design cost and how to make the process more fluid.
What's The Average Cost for an App?
Skipping the factors in the app's cost breakdown, it can it can cost around $80,000-$250,000 depending on its features, platform, and quality. Online app calculators give an average between $200,000 and $350,000 to create an app with multiple features.
Native iOS and Android apps are usually fast, large, and are optimized to provide the best user experience. Also, they're created using built-in APIs and processes that have a multitude of features.
Depending on how many people you need for your development team and the amount of platforms, native app design costs can be very expensive. Regardless of what you're going to go with, your app's features will determine its total cost.
Before committing and engaging to an offshore development company, you have to do some homework first. This means that you'll have to look up the company and check for its reputation, reviews, awards and track record. Since this project might cost around $10,000+ or more, it's important to look at this price carefully.
It's also helpful to seek out their past clients and speak on the company's experience. In fact, you can take it a step further and meet the development team in person. When doing this, make sure that you speak to their designers as well.
After they give you a quote for the cost of their app, always add at least 15%-25% extra to the initial cost in order to reduce the risk. This is because developing apps isn't a straightforward process and there are unexpected hurdles that occur along the way.
Basically, the app design cost depends on what you're trying to achieve. You'll have to plan out exactly what apps you want your designers to create. Ultimately, set up a budget to make your apps to ensure that your project will be completed correctly!
Best Android games– The 25 best mobile games to download on your … only have the top apps, so bookmark this page to keep up to date!


Ready to take a step into oscilloscope diagnostics, but don't know where to start?
Starting from Step 1 (Oscilloscope Diagnostics, A PicoScope Guide), we've created a 5 step training programme to guide those new to PicoScope along their journey of scope diagnostics from the very beginning.
As you progress through the training programme, you will learn PicoScope from our basic tests through to our more advanced tests and accessories. The Steps are designed to progress your learning at a steady rate, teaching PicoScope from the ground up. Completing our 5 Steps to Success training programme will give you the confidence to master your PicoScope, and diagnostic skills.
Whether you want to take part in, or run one of our 5 Steps to success training courses, please Contact us for more information.
Starting scope diagnostics gives a basic overview and introduction to PicoDiagnostics, PicoScope 6 Automotive, and the PicoScope unit you will be using. It covers details such as voltage vs time, toolbars, and of course the benefits of scope diagnostics. Its main focus is on the user interface of the software, and has detailed information about various features.
The book also incorporates the practical tests in focus during the training, and encourages a hands-on approach.
Advanced scope diagnostics gives an overview of the topics covered in Step 2, and moves on to cover topics such as: manual setup, viewing multiple signals, scaling, measuring, filtering, math channels, masks, alarms and more.
This book also incorporates the practical tests discussed during the training and encourages a hands-on approach.
Pressure testing with the WPS500X gives a basic overview and introduction to the WPS500X unit, the applications for it and how to use it. It will also incorporate the practical tests in focus during the training. The ability to measure pressure against time, allows us to see rapid events taking place that were never visible before.
The WPS500X pressure transducer takes diagnostics to a whole new level.
Noise and vibration testing gives a specific look into the PicoDiagnostics NVH products, NVH theory, our software and the techniques involved in analyzing the data you capture.
PicoDiagnostics is an automotive fault-finding software package for your PicoScope oscilloscope, turning your PC/laptop into a multifunctional diagnostics tool. It includes a range of in-built tests that are easy to operate, such as compression tests, battery and alternator tests, cylinder balance, and NVH.
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Complete with Written Exam booklets and completion certificates, Pico now offer trainers the ability to run a Pico endorsed course.


Have you ever imagined that a smartphone can be a lot cheaper than a pizza?
Have you ever imagined that a day will come when the micro SD card that you smartphone supports is 4-5 times of the price of your smartphone? Yes, it's too hard to even imagine but that's the reality, a smartphone at just Rs. 251 which is about $4 USD! Ringing Bells company announced the cheapest ever smartphone Freedom 251, in India at Rs. 251! Even a low end basic feature phone costs more than Rs. 251 but Freedom 251 is a fully functional Android smartphone running Android 5.1 Lollipop. Simply unbelievable! The phone is a product of the Make in India Initiative, which mainly aims to popularize and provide nation made products to the people.
4. A 1450 mAh battery gives you freedom to talk, text, Play and watch videos. The main focus is to provide extended power for people who live in remote areas with shortage of power and electricity.
5. 3G internet connectivity support.
6. 3.2 MP primary camera with .3 MP front facing camera to capture your special moments.
7. Runs Android 5.1 Lollipop.
8. 1 year of Warranty.
Ringing Bells Pvt. Ltd has already announced of launching more than 650 service centers in India. This is not just an affordable smartphone but it's a revolution of circulating technology and gadgets among the people who, otherwise, couldn't have afforded a smartphone. In this context it's remarkable to mention that Freedom 251 comes with some pre-installed Apps like Woman Safety, Swachch Bharat (Clean India initiative), Fisherman, Farmers, Medical, PlayStore, WhatsApp, Facebook, YouTube and many more. this will reduce the initial cost of downloading Apps.
You can book your phone online and check more about Freedom 251 from here.
Freedom251's website is currently getting more than 600k hits per second. So online ordering of Freedom251 is temporarily on hold as they are upgrading their servers. They have promised to resume the online booking within or before 24 hour.


Being that Dallas is a booming city that continues to grow, there is a substantial need for a wide range of zip codes. Dallas has a great number of zip codes, since the city is so large. Additionally, more are being added as the city grows.


Tenant advocates are hoping a change in the state legislature will lead to sweeping reform of rent stabilization laws.
With midterm elections looming, I'm curious how having new representatives in the New York State legislature might impact rent stabilization laws in the city.
Much depends on how the State Senate races turn out, says Sam Himmelstein, a lawyer who represents residential and commercial tenants and tenant associations, but tenant advocates are pushing for several changes to rent stabilization law that could come to pass if Democrats take over the legislature.
Closing the preferential rent loophole: Some landlords of rent-stabilized apartments offer tenants a "preferential rent" that is lower than the legal rent. However, these rents are not subject to the law that limits by how much stabilized rents can be increased each year, so when these tenants renew their leases, the landlords can then raise their rents by substantial amounts. Eliminating this loophole would make the preferential rent the base rent for all future increases, and thus prevent landlords from attracting tenants with a more affordable-seeming rent, and then surprising them upon lease renewal.
Ending vacancy increases: State law permits landlords of stabilized apartments to increase the rent by 20 percent when a new tenant moves into a vacated apartment and signs a two-year lease, or by 19.25 percent if a new tenant signs a one-year lease. Tenant advocates argue that this is too high, encourages landlords to evict tenants, and should be ended.
MCI and IAI reform: Major Capital Improvements and Individual Apartment Improvements are substantial renovations that landlords make to apartment buildings or to individual units, which then enables them to raise the rent on stabilized units by a percentage based on the cost of the updates. "There have been all different kinds of reforms proposed," Himmelstein explains. "One is to make MCIs a temporary surcharge instead of a permanent rent increase, and once landlord is paid back for their work, it would end. There are also proposals to tighten the definitions of what counts as an MCI or IAI." Another possible reform to MCIs and IAIs would be to extend the amortization period, so that monthly rent increases would be reduced. In addition, the current 50 percent offset for landlords who receive J-51 tax benefits could be increased to 100 percent, and a mechanism established to require the state housing agency to verify the J-51 benefit before granting the rent increase. This is important because currently there is no enforcement or coordination between state and city agencies, and many landlords get away with "double-dipping," that is collecting both full MCI rent increases and J-51 tax benefits.
Ending MCI rent increases: Another bill proposes to end MCI rent increases entirely and grant landlords tax subsidies instead. And a bill is being drafted that would simply bar rent hikes for building-wide improvements, without any tax benefits to the landlord. Given the recent expose of how the Trump family used fraudulent bills to inflate MCI rent increases for their rent-regulated tenants, a change in the state legislature could mean new laws that eliminate or vastly reduce MCIs.
Mitchell-Lama reform: Mitchell-Lama buildings provide affordable rentals and co-ops to low and moderate-income New Yorkers, but currently, when these buildings leave the Mitchell-Lama program, only those built before 1974 go into rent stabilization, while the rest turn market-rate. A change in state leadership could mean reforming this program so that all Mitchell-Lama apartments, regardless of their date of construction, would become rent-stabilized. Post-1973 Mitchell-Lama and project-based Section 8 buildings would be covered by the bill. The bill also bars the use of "unique or peculiar circumstances" as the basis for a rent increase when a building transitions from Mitchell-Lama or Section 8 to rent stabilization.
Allowing more municipalities to opt into rent-stabilization: "There is legislation being considered that would allow any municipality in the state to opt into rent regulation, as opposed to just New York, Westchester, Rockland and Nassau Counties," Himmelstein says. Currently, those are the only New York State municipalities with rent stabilization laws in place.
Greater eviction protection: Another bill pending in the state legislature, Himmelstein says, would give tenants in small buildings not subject to rent-stabilization greater protection from being asked to move out when their leases expire. "Landlords could only do good-cause eviction of tenants," he explains.
Lowering rent increases on rent-controlled apartments: Currently, tenants of rent-controlled apartments pay higher annual rent increases than those of rent-stabilized apartments; pending legislation would lower those increases.
Read all our Ask a Renters Rights Lawyer columns here.
Sam Himmelstein, Esq. represents NYC tenants and tenant associations in disputes over evictions, rent increases, rental conversions, rent stabilization law, lease buyouts, and many other issues. He is a partner at Himmelstein, McConnell, Gribben, Donoghue & Joseph in Manhattan. To submit a question for this column, click here. To ask about a legal consultation, email Sam at [email protected] or call (212) 349-3000.


We would like to cordially welcome you to the Bauernhof Zieferhof .
Parking is not a problem at our hotel, we have ample parking available for our guests.
You don't want to leave your four-legged friends at home while travelling? No problem with this quaint hotel - just bring them along!
If you enjoy skiing, you'll love that many ski-possibilities are offered next to our hotel.


THE CADOGAN HOTEL, 75 SLOAN STREET, LONDON, SW1X 9SG.
The Cadogan Hotel has been serving a traditional Afternoon Tea since 1887 and one very famous celebrity, Oscar Wilde, was a frequent visitor.
At the moment they are offering a Winter Afternoon Tea for just £15, which includes a free glass of Champagne. The Hotel is in the heart of London's Knightsbridge district so ideal for visiting the Winter Sales.
The offer is available Monday to Friday from 12pm – 6pm until 31st January 2011. So don't try and get the offer at a weekend and don't forget the discretionary service charge of 12.5%.
< Previous BEVERLEY ARMS HOTEL, 25 NORTH BAR WITHIN, BEVERLEY, EAST YORKSHIRE, HU17 8DD.
it is very old and has serious need of remodernisation with the guest rooms …..
Im sure the tea is yummy though!!
Really Julie, well if you did pop in for £15 deal do tell them where you found out about it.
and my local schools are still there…. Look them up if you wish…..
And then to St Thomas Moore secondary in Cadgoan Street!!


text:
\section{Introduction}

For the past decade, deep learning has gained great success in image recognition, natural language processing,  computer vision, and other numerous practical applications in our daily life. Until very recently, it begins to draw much attention to solve partial differential equations (PDEs) using deep neural network (DNN) in scientific computing community. Part of the theoretical reason can be attributed to the various kinds of expressive power for function approximations using DNN such as those described in \cite{Cybenko1989, HSW89, LPWHW17, HS18}, just to name a few.  A usage of automatic differentiation in machine learning \cite{BPRS18} making derivatives evaluations through neural network much easier is probably another reason in practice.
However, from the authors' points of view, the most motivated reason could be when the PDEs become intractable to traditional numerical methods such as finite difference, finite element, or spectral method. For instance, even with today's
growing computing power and resources, solving high-dimensional PDEs is still notoriously difficult to the above traditional numerical methods due to the ``curse of dimensionality". Some successful solving high-dimensional PDEs using deep learning approach can be found in \cite{Weinan_2018_2, DGM_2018, ROLNF20}, just to name a few.

As deep learning network to solve PDEs becomes popular, there are mainly two different approaches; namely, the physics-informed neural networks (PINNs)~\cite{raissi2019}, and the deep Ritz method~\cite{weinan_2018}. The former one
is introduced for function approximation and is trained by minimizing the mean squared error loss of the equation residual, and initial and boundary condition errors as well. The deep Ritz method, however, begins with solving the variational problem equivalent to the original PDE so the natural loss function in this framework is simply the energy functional. Both DNN approaches share the same major mesh-free advantage which is unlikely to have by using traditional numerical methods.
As a result, the implementation of the deep neural network to solve problems on complex geometry~\cite{PFNN_2021} and in  high-dimensional space ~\cite{Weinan_2018_2, DGM_2018} can be performed feasibly.

Despite of the success of deep learning approach in solving PDEs with smooth solutions, not much attention had been paid to problems with non-smooth solution, or the solution is only smooth in a piecewise manner. A typical example is the elliptic interface problem where the solution and its derivatives have jump discontinuities across the interface.
The main difficulty might due to the fact that the activation function in a deep neural network is in general smooth, such as the sigmoid function, or at least continuous such as the rectified linear unit (ReLU).
Along this line, a deep Ritz type approach to solve the elliptic interface problem with high-contrast discontinuous coefficients is developed in ~\cite{wang_2020}. The network architecture is similar to the one proposed in \cite{weinan_2018}
where two fully-connected hidden layers compose a block so the network consists of two blocks with an output linear layer. Each block is linked by a residual connection. However, there lacks of intuitive explanation on why such network is constructed. Another deep least squares method~\cite{DLS_2020} is proposed to minimize the first-order system least-squares functional which is rewritten from the second-order elliptic problem. An  accuracy comparison using different loss functions and activation functions are performed in detail. However, the results are presented in only one-dimensional problems. Notice that, the solutions in both papers \cite{wang_2020, DLS_2020} are continuous but the derivatives have jumps across the interface.

To the best of our knowledge, so far the most successful methodology for solving elliptic problems with discontinuous solution and derivatives across the interface is to use the piecewise deep neural network proposed by He et al. ~\cite{he2020meshfree}. They approximate the solution by two neural networks corresponding to two disjoint subdomains so that in each subdomain, the solution remains smooth. These two networks are linked by imposing the solution and its normal derivative jump conditions in the mean squared error loss. In this way, the resulting error of the training solution can be significantly reduced.  However, like most DNN, as the network becomes deeper, the training process requires more efforts. Not to mention that, one has to train one individual neural network on each subdomain.

In this paper, we propose a new discontinuity capturing shallow neural network (DCSNN) for solving elliptic interface problems. The novelty of the proposed network are three-folds. Firstly, the network captures the solution and its normal derivative jumps sharply across the interface. Secondly, the network is completely shallow meaning that only one hidden layer is needed so it significantly reduces the training cost in contrast to DNN. Lastly, it is totally mesh-free meaning that it can be applied
to solve the problems with more complex (or irregular) domains which the traditional accurate immersed interface method (IIM)~\cite{Li2006} is hard to implement, especially in higher dimensions.

The rest of the paper is organized as follows. In Section~2,  we show how a $d$-dimensional piecewise continuous function
can be approximated by the present shallow network. It demonstrates the main underlying idea of the developed DCSNN by function approximation. Then an optimization algorithm to train the network is introduced followed by an example to confirm the accuracy. The present network for the elliptic interface problem is presented in Section~3, followed by a series of
numerical accuracy tests and comparisons in Section~4.
Some concluding remarks and future work are given in Section~5.

\section{Discontinuity capturing shallow neural network}

In this section, we start with constructing a neural network to approximate a $d$-dimensional, \emph{piecewise continuous}, scalar function $\phi(\mathbf{x})$ in the domain $\Omega = \Omega^-\cup\Omega^+ \cup \Gamma$ ($\Omega\subseteq\mathbb{R}^d$) defined by
\begin{align}
\phi(\mathbf{x}) =
\left\{
\begin{array}{ll}
\phi^-(\mathbf{x})  & \mbox{if\;\;} \mathbf{x} \in \Omega^-,\\
\phi^+(\mathbf{x}) & \mbox{if\;\;} \mathbf{x} \in \Omega^+,
\end{array}\right.
\end{align}
where $\mathbf{x} = (x_1,x_2,\cdots,x_d)$, $\phi^-$ and $\phi^+$ are both smooth functions in their corresponding subdomains. The interface $\Gamma$ is defined as the boundary between the subdomains $\Omega^-$ and $\Omega^+$, where the function $\phi$ has a jump discontinuity at $\Gamma$. (Note that, the function value of $\phi$ at the interface $\Gamma$  is simply defined by $\phi^-$ for convenience purpose.)  In order to approximate the above piecewise continuous function in $d$ dimensions, we first make a continuous extension of the function in $d+1$ dimensional space, and then construct a shallow (one hidden layer) neural network to approximate such a function. Since we aim to approximate the piecewise continuous function accurately and capture the function discontinuity sharply using only a one hidden layer neural network; hereby, we call the present network approximation as the Discontinuity Capturing Shallow
Neural Network (DCSNN) afterwards.

\subsection{Continuous function extension}

The key idea is that, a $d$-dimensional discontinuous function can be alternatively represented by a $(d+1)$-dimensional smooth function.
To this end, we first introduce an augmented one-dimensional variable $z$ to categorize the variable $\mathbf{x}$ into two types; namely, $\mathbf{x}$ in $\Omega^-$ or $\Omega^+$.
More precisely, we set $z = -1$ if $\mathbf{x}\in\Omega^-$ and $z = 1$ if $\mathbf{x}\in\Omega^+$ (this task can be easily done with the help of a level set function).
We then define the $(d+1)$-dimensional function using the augmentation variable $(\mathbf{x},z)$ as
\begin{align}
\phi_{aug}(\mathbf{x},z) =
\left\{
\begin{array}{ll}
\phi^-(\mathbf{x})  & \mbox{if\;\;} z = -1,\\
\phi^+(\mathbf{x}) & \mbox{if\;\;} z = 1,
\end{array}\right.
\end{align}
where $\mathbf{x}\in \Omega$ and $z\in \mathbb{R}$.
That is, both $\phi^-$ and $\phi^+$ are regarded as smooth extension over the entire domain $\Omega$, and the augmented function $\phi_{aug}(\mathbf{x},z)$ is assumed to be continuous on the domain $\Omega\times\mathbb{R}$. In such way,
 the function $\phi$ can be rewritten in terms of the augmented function as
\begin{align}\label{Eq:augphi}
\phi(\mathbf{x}) =
\left\{
\begin{array}{ll}
\phi_{aug}(\mathbf{x}, -1) & \mbox{if\;\;} \mathbf{x} \in \Omega^-,\\
\phi_{aug}(\mathbf{x}, 1)  & \mbox{if\;\;} \mathbf{x} \in \Omega^+.\\
\end{array}\right.
\end{align}
Therefore, the piecewise continuous function $\phi$ now can be regarded as a continuous function defined on one-dimensional higher space and restricted to its subdomain.

We illustrate this idea by considering a one-dimensional example where $\phi^-(x) = \sin(2\pi x)$ if $x\in[0,\frac{1}{2}]$ and $\phi^+(x) = \cos(2\pi x)$ if $x\in(\frac{1}{2},1]$.
The function has a jump discontinuity at $x=\frac{1}{2}$, see Fig.~\ref{Fig:phi_aug}(a).
The two-dimensional augmented function can be constructed as $\phi_{aug}(x,z) = \fr{1-z}{2}\phi^-(x) + \fr{1+z}{2}\phi^+(x)$, see Fig.~\ref{Fig:phi_aug}(b) for the function profile. In particular, its restriction at $z=-1$ corresponding to $\phi^-$ is shown as blue solid curve, and the one at $z = 1$ corresponding to $\phi^+$ is shown as red solid curve. It is important to mention that this augmented approach can be straightforwardly applied to piecewise continuous functions with arbitrary many pieces by simply labelling various $z$ values. Besides, the augmented function is not unique, i.e., there exists infinitely many such a function that has its restriction to be $\phi$.
The remaining issue is how to construct the augmented function using an approximation of neural network and train the network efficiently, which we  describe in the next subsection.

\begin{figure}[h]
\centering
\includegraphics[scale=0.33]{phi_aug.png}
\caption{(a) The one-dimensional piecewise continuous function $\phi(x)$.
(b) The two-dimensional augmented function $\phi_{aug}(x,z)$ at different $z$ values.
}
\label{Fig:phi_aug}
\end{figure}

\subsection{Shallow neural network structure}\label{subsec:SINN}

In this subsection, we propose a shallow neural network to approximate a $d$-dimensional piecewise continuous function.
As shown in the previous subsection, all we have to do is to construct the augmented function $\phi_{aug}$ that is in fact continuous in $d+1$ dimensions.
Based on the universal approximation theory~\cite{Cybenko1989}, we hereby design a \emph{shallow}, \emph{feedforward}, \emph{fully-connected} neural network architecture, in which only one single hidden layer is employed to approximate $\phi_{aug}$.
The structure of this shallow neural network  is shown in Fig.~\ref{Fig:SINN}.
Let $N$ be the number of neurons used in the hidden layer, the augmented function (or output layer) under this network structure can be explicitly expressed by
\begin{align}\label{Eq:SINN}
\phi_{aug}(\mathbf{x},z) = W^{[2]}\sigma(W^{[1]}(\mathbf{x},z)^T+b^{[1]}) + b^{[2]},
\end{align}
where $W^{[1]}\in\mathbb{R}^{N\times(d+1)}$ and $W^{[2]}\in\mathbb{R}^{1 \times N}$ being the weights, $b^{[1]}\in\mathbb{R}^{N}$ and $b^{[2]}\in\mathbb{R}$ being the biases, and $\sigma$ is the activation function. One can easily see that the augmented function is simply a finite linear combination of activation functions.

\begin{figure}[h]
\centering
\includegraphics[scale=0.35]{SINN.pdf}
\caption{The structure of DCSNN. $N$ neurons are used in the hidden layer.}
\label{Fig:SINN}
\end{figure}

By collecting all the training parameters (including all the weights and biases) in a vector $\mathbf{p}$, the total number of parameters in the network (i.e., dimension of $\mathbf{p}$) is counted by $N_p = (d+3)N + 1$.
Given $M$ training points $\{(\mathbf{x}^i,z^i)\}^M_{i=1}$, where $z^i$ is determined by identifying the category of $\mathbf{x}^i$, and target outputs $\{\phi(\mathbf{x}^i)\}^M_{i=1}$, these parameters in $\phi_{aug}$ are learned via minimizing the following mean squared error loss
\begin{align}\label{Eq:loss}
\mbox{Loss}(\mathbf{p}) = \fr{1}{M}\sum_{i = 1}^M\left( \phi(\mathbf{x}^i) - \phi_{aug}(\mathbf{x}^i,z^i;\mathbf{p}) \right)^2.
\end{align}

Now, we are in a position to solve the above optimization problem.
Since the present shallow network generally results in a moderate number of training parameters, the above optimization problem can be efficiently solved by Levenberg-Marquardt method~\cite{Marquardt63}, a full-batch optimization algorithm. That is, we find $\mathbf{p}$ via the iterative procedure
\begin{align}\label{Eq:LM}
\mathbf{p}^{(k+1)} = \mathbf{p}^{(k)} + \left( J^TJ + \mu I \right)^{-1}\left[ J^T\left(\Phi-\Phi_{aug}(\mathbf{p}^{(k)})\right) \right],
\end{align}
where the $i$th component of the vectors $\Phi$ and $\Phi_{aug}$ correspond to $\phi(\mathbf{x}^i)$ and $\phi_{aug}(\mathbf{x}^i,z^i;\mathbf{p})$ in the loss function (\ref{Eq:loss}), and $J\in\mathbb{R}^{M\times N_{p}}$ (typically $M>N_p$) is the Jacobian matrix given by $J = \partial\Phi_{aug}/\partial\mathbf{p}$.
The computation of Jacobian matrix can be done using automatic differentiation \cite{BPRS18, GW08}, or back propagation algorithm.
Notice that $\mu$ is the damping parameter. The general strategy of tuning the damping parameter is as follows. Initially, $\mu$ is set to be large so that first few updates are small steps along gradient direction (note that the term $J^T\left(\Phi-\Phi_{aug}(\mathbf{p})\right)$ denotes the negative gradient direction of loss function). The descent of loss function suggests tuning $\mu$ to be small, in such a way, the Levenberg-Marquardt method approaches the Gauss-Newton method, and the solution of the optimization problem typically accelerates to the local minimum. The major cost in each iteration step (\ref{Eq:LM}) comes from the computation of matrix-vector multiplication. This can be done efficiently by using reduced singular value decomposition to the Jacobian matrix $J = U\Sigma V^T$ so that the updating direction (the second term on the right-hand side of Eq.~(\ref{Eq:LM})) is computed by $V\mbox{diag}(\fr{\sigma_J}{\sigma_J^2+\mu})U^T(\Phi-\Phi_{aug})$, where $\sigma_J$ denotes the singular values of $J$.

\subsection{An example of function approximation}

For illustration purpose,
here we show the capability of the present network by considering the one-dimensional piecewise continuous function
\begin{align}
\phi(x) =
\left\{
\begin{array}{ll}
\sin(2\pi x)  & \mbox{if\;\;} x \in [0,\fr{1}{2}],\\
\cos(2\pi x) & \mbox{if\;\;} x \in (\fr{1}{2},1].
\end{array}\right.
\end{align}
The network is trained by using only $5$ neurons in the hidden layer, thus there are totally $21$ parameters in weights and biases needed to be learned.
We use $100$ randomly sampled training points in the interval $[0,1]$ (including two boundary points) with the sigmoid activation function and stop the iteration when $\mbox{Loss}(\mathbf{p}) < 10^{-12}$.

The result is shown in Fig.~\ref{Fig:1d_SINN}. In panel (a) we compare the exact solution $\phi$ with the trained DCSNN model, denoted by $\phi_\mathcal{S}$. One can see that they coincide quite nicely with each other. It also clearly shows that a jump discontinuity at $x=0.5$ is captured sharply.
We also show in panel (b) the pointwise absolute error $|\phi_\mathcal{S}-\phi|$.
We note that the maximum error occurs close to the domain boundary rather than at the point of discontinuity.
The prediction of the present network is quite accurate where the maximum norm of the error is of magnitude $O(10^{-7})$.
It is important to mention that, despite only one-dimensional case is presented here, discontinuous functions in higher dimensions can also be approximated accurately and efficiently using the present network structure (see the last example in Section 4).

\begin{figure}[h]
\centering
\includegraphics[scale=0.4]{1d_SINN.pdf}
\caption{(a) The piecewise continuous function $\phi$ (solid line) and the trained DCSNN model $\phi_\mathcal{S}$ (dotted points). (b) The absolute error $|\phi_\mathcal{S}-\phi|$. The maximum error is $\|\phi_\mathcal{S}-\phi\|_\infty = 5.402\times10^{-7}$.}
\label{Fig:1d_SINN}
\end{figure}

\section{Elliptic interface problems}

Now we apply the DCSNN to solve $d$-dimensional variable coefficient elliptic interface problems. In such problem, a domain $\Omega \subset \mathbb{R}^d$ is divided by an embedded interface $\Gamma \subset \mathbb{R}^{d-1}$ into two regions, namely, inside ($\Omega^-$) and outside ($\Omega^+$) of the interface, so that $\Omega = \Omega^- \cup \Omega^+ \cup \Gamma$.
The elliptic interface equation with general inhomogeneous jump conditions reads
\begin{align}\label{Eq:elliptic}
\nabla\cdot(\beta\nabla\phi) = f \quad \mbox{in }\Omega \setminus \Gamma, \quad [\phi]=v, \quad [\beta\partial_n\phi]=w, \quad \mbox{on }\Gamma,
\end{align}
where the variable coefficient is defined by $\beta = \beta^-$ in $\Omega^-$ and $\beta = \beta^+$ in $\Omega^+$.
Here the bracket $[\cdot]$ denotes the jump discontinuity of the quantity approaching from $\Omega^+$ minus the one from $\Omega^-$, $\mathbf{n}$ stands for the outward normal vector defined on the interface $\Gamma$ and $\partial_n\phi$ is the shorthand notation for $\nabla\phi\cdot\mathbf{n}$.
Certainly, the above differential equation should be accompanied with suitable boundary conditions (say Dirichlet or Neumann) along the domain boundary $\partial\Omega$.
Throughout this paper we will focus on the case of Dirichlet boundary condition $\phi|_{\partial\Omega} = g$, while other types of boundary conditions will not change the main ingredients presented here.
For simplicity, we assume that $\beta$ has sufficient smoothness on $\beta^-$ and $\beta^+$, and $|\beta| \ge\epsilon>0$.
Hence we can simply rewrite Eq.~(\ref{Eq:elliptic}) in the form of the Poisson equation:
\begin{align}\label{Eq:Poisson}
\Delta\phi = \tilde{f} =
\left\{
\begin{array}{ll}
f^-/\beta^-   & \mbox{if\;\;} \mathbf{x}\in \Omega^-\\
f^+/\beta^+ & \mbox{if\;\;} \mathbf{x} \in \Omega^+\\
\end{array}\right.,  \quad  [\phi]=v, \quad [\beta\partial_n\phi]=w, \quad \mbox{on }\Gamma.
\end{align}
We then introduce a $(d+1)$-dimensional augmented function $\phi_{aug}(\mathbf{x}, z)$ that satisfies
\begin{align}\label{Eq:Poisson_aug}
\Delta_{\mathbf{x}}\phi_{aug}(\mathbf{x}, z)  =
\left\{
\begin{array}{ll}
f^-/\beta^- & \mbox{if\;\;} \mathbf{x}\in\Omega^-,\, z = -1\\
f^+/\beta^+ & \mbox{if\;\;} \mathbf{x}\in\Omega^+,\, z = 1\\
\end{array}\right.,  \quad  [\phi_{aug}] =v, \quad [\beta\partial_n\phi_{aug}]=w, \quad \mbox{on }\Gamma,
\end{align}
where the jump condition is evaluated by taking the difference between values at $z=1$ and $z=-1$, i.e., $[\phi_{aug}]= \phi_{aug}(\mathbf{x}, 1) - \phi_{aug}(\mathbf{x}, -1)$ for $\mathbf{x}\in\Gamma$, and the same manner applies for $[\beta\partial_n\phi_{aug}]$ (note that $\partial_n\phi_{aug} = \nabla_{\mathbf{x}}\phi_{aug}\cdot\mathbf{n}$). Once $\phi_{aug}$ is found, the function $\phi$ is recovered using Eq.~(\ref{Eq:augphi}).

Now we need to solve the augmented elliptic interface problem (\ref{Eq:Poisson_aug}) to obtain $\phi_{aug}$ using the present DCSNN.
Given training points in $\Omega$, on the domain boundary $\partial\Omega$ and along the embedding interface $\Gamma$,
denoted by $\{(\mathbf{x}^i, z^i)\}_{i=1}^M$, $\{\mathbf{x}^j_{\partial\Omega}\}_{j=1}^{M_b}$ and $\{\mathbf{x}^k_{\Gamma}\}_{k=1}^{M_\Gamma}$, respectively,
we hereby solve the equation (\ref{Eq:Poisson_aug}) by minimizing the mean squared error loss in the framework of physics-informed learning technique~\cite{raissi2019}
\begin{align}\label{Eq:loss_PINN}
\begin{split}
\text{Loss}(\mathbf{p}) & =  \frac{1}{M}\sum_{i = 1}^M \left( \Delta_\mathbf{x}\phi_{aug}(\mathbf{x}^i,z^i) - \tilde{f}(\mathbf{x}^i) \right)^2
+ \frac{\alpha_b}{M_b}\sum_{j = 1}^{M_b} \left( \phi_{aug}(\mathbf{x}^j_{\partial\Omega},1) - g(\mathbf{x}^j_{\partial\Omega}) \right)^2\\
& + \frac{\alpha_\Gamma}{M_{\Gamma}}\sum_{k = 1}^{M_\Gamma} \left( [\phi_{aug}(\mathbf{x}^k_\Gamma)] - v(\mathbf{x}^k_\Gamma) \right)^2 + \frac{\alpha_\Gamma}{M_{\Gamma}}\sum_{k = 1}^{M_\Gamma} \left( [\beta\partial_n\phi_{aug}(\mathbf{x}^k_\Gamma)] - w(\mathbf{x}^k_\Gamma) \right)^2,
\end{split}
\end{align}
where $\alpha_b$ and $\alpha_\Gamma$ are positive constants that can be adjusted to strengthen or weaken the contribution of accuracy on the domain boundary or at the interface, respectively.
Notice that, in the above equation we have collected all training parameters (weights and biases) in the vector $\mathbf{p}$.
Since the least squares loss is adopted, again it could be quite efficient to train the neural network using the Levenberg-Marquardt method as introduced in Subsection~\ref{subsec:SINN}. We mention that the spatial derivatives of the target function $\phi_{aug}$ in the loss function, Eq.~(\ref{Eq:loss_PINN}), can be computed by automatic differentiation easily. Although the present network is similar in spirit to PINNs \cite{raissi2019},
here we only use one hidden layer with sufficiently small number of neurons so it reduces the computational complexity and learning workload significantly without sacrificing the accuracy. Moreover, as shown in some examples in next section, the present DCSNN not only achieves better accuracy than the traditional finite difference method such as immersed interface method \cite{Li2006, Hu2015, Hsu2019} in solving Eq.~(\ref{Eq:elliptic}) but also outperforms other piecewise DNN \cite{he2020meshfree} in terms of accuracy and network complexity.

\section{Numerical results}
In this section, we use the developed network to perform several numerical tests for the elliptic interface problems, in two, three, and even six dimensions. Throughout all the examples (except Example~2 in which we  compare our results with existing literature), we set $\beta^- = 1$ and $\beta^+ = 10^{-3}$ (so $\beta^-/\beta^+  = 10^3$, the problem with high contrast coefficients), and the penalty parameters $\alpha_b=\alpha_\Gamma = 1$. The exact solution with $d$-dimensional variable $\mathbf{x} = (x_1,x_2,\cdots,x_d)$ is given by
\begin{align}
\phi(\mathbf{x}) =
\left\{
\begin{array}{ll}
\prod\limits_{i=1}^d \exp(x_i) & \mbox{if\;\;} \mathbf{x} \in \Omega^-,\\
\prod\limits_{i=1}^d \sin(x_i)  & \mbox{if\;\;} \mathbf{x} \in \Omega^+,\\
\end{array}\right.
\end{align}
so one can easily obtain the corresponding right-hand side function $\tilde{f}$, and the jump information $v$ and $w$ in Eq.~(\ref{Eq:Poisson}) through the above solution.

In the following examples, we choose sigmoid as the activation function, and we terminate training procedure when the stopping criteria $\mbox{Loss}(\mathbf{p}) < \varepsilon$ is fulfilled (the tolerance $\varepsilon$ is set to be at least smaller than $10^{-9}$).
After the training process is finished, we use the cross-validation used in machine learning practice to check the accuracy. That is, we measure the accuracy of the solution using the testing error instead of training error. By doing so, we randomly choose $N_{test}$ testing points lying in $\Omega$ by computing the $L_\infty$  and $L_2$ norm as
\begin{align*}
\|\phi_\mathcal{S}-\phi\|_\infty = \max_{1\leq i \leq N_{test}}|\phi_\mathcal{S}(\mathbf{x}^i)-\phi(\mathbf{x}^i)|, \quad
\|\phi_\mathcal{S}-\phi\|_2 = \sqrt{\frac{1}{N_{test}}\sum_{i=1}^{N_{test}}(\phi_\mathcal{S}(\mathbf{x}^i)-\phi(\mathbf{x}^i))^2},
\end{align*}
where $\phi_\mathcal{S}$ is the function obtained by the present DCSNN.
In general,  we set the testing number $N_{test}=100M$, where $M$ is the number of training points in $\Omega$.

\paragraph{\textbf{Example 1}}

We begin with the example by considering the problem in two dimensions.
In this test, the regular square domain $\Omega = [-1, 1]\times [-1, 1]$ is considered while the interface is chosen as an ellipse $\Gamma:\left(\displaystyle\frac{x_1}{0.2}\right)^2+\left(\displaystyle\frac{x_2}{0.5}\right)^2=1$.
We use total $128$ training points ($M=64$ interior points in the computational domain, $M_b=32$ points on the boundary, and $M_\Gamma=32$ points on the interface).

It is interesting to see that the deployment of training data can indeed affect the accuracy of DCSNN solutions.
We consider three different training point distributions; namely, the Chebyshev points of the first kind \cite{Trefethen2000}, uniformly distributed, and randomly chosen points.
The training points on $\Omega$ and $\partial\Omega$ are chosen based on those three distributions, while the points at the interface $\Gamma$ are chosen randomly.
The results are shown in Table~\ref{Table:exp1_node} where two sets of neurons $N=10, 20$ are used for comparison.
We find that the errors obtained by Chebyshev and uniform nodes are in general of the same order of magnitude, whereas the ones obtained by random distribution are less accurate. The corresponding pointwise errors are shown in Fig.~\ref{Fig:EX1_error}.
As one can see, the major error of Chebyshev nodes comes from the vicinity of the interface, while the other two distributions have their maximum error occurs close to the corners of the domain.
This finding is somewhat surprising in the sense that, even though the activation function is fairly different from polynomials, the approximation still achieves better accuracy on Chebyshev nodes.

\begin{table}[h]
\centering
\begin{tabular}{@{}c@{\hspace{10pt}}c@{\hspace{10pt}}c@{\hspace{5pt}}c@{\hspace{10pt}}c@{\hspace{10pt}}c@{\hspace{5pt}}c@{\hspace{10pt}}c@{\hspace{10pt}}c@{\hspace{5pt}}}
\hline
\multirow{2}{*}[-3pt]{$(N,\, N_p)$} & \multicolumn{2}{c}{Chebyshev nodes} & & \multicolumn{2}{c}{uniform nodes} & & \multicolumn{2}{c}{random nodes}\\
\cmidrule(){2-3}\cmidrule(){5-6}\cmidrule(){8-9}
    & $\|\phi_\mathcal{S}-\phi\|_\infty$ & $\|\phi_\mathcal{S}-\phi\|_2$ & & $\|\phi_\mathcal{S}-\phi\|_\infty$ & $\|\phi_\mathcal{S}-\phi\|_2$ & & $\|\phi_\mathcal{S}-\phi\|_\infty$ & $\|\phi_\mathcal{S}-\phi\|_2$\\
\midrule
(10, 51)   & 3.005E$-$06 & 3.515E$-$07 & & 9.105E$-$06 & 8.745E$-$07 & & 1.631E$-$05 & 1.370E$-$06 \\
(20, 101) & 2.490E$-$07 & 2.604E$-$08 & & 8.179E$-$07 & 4.810E$-$08 & & 3.442E$-$06 & 3.041E$-$07 \\
\hline
\end{tabular}
\caption{The errors with different distributions of training data.}
\label{Table:exp1_node}
\end{table}

\begin{figure}[h]
\centering
\includegraphics[scale=0.38]{EX1_error.png}
\caption{The pointwise error $|\phi_\mathcal{S}-\phi|$ using $N = 20$ with different training data distributions.}
\label{Fig:EX1_error}
\end{figure}

The solution profile of DCSNN is shown in Fig.~\ref{Fig:EX1}.
One can see that the solution captures precisely the discontinuous feature sharply.
Meanwhile, it is interesting to see that, the error between the exact and the present solutions also shows a discontinuity across the interface due to the intrinsic construction of the present network, where the three-dimensional augmented function is trained.

\begin{figure}[h]
\centering
\includegraphics[scale=0.38]{EX1_solution.png}
\caption{Left: The DCSNN solution profile. Right: Absolute error between DCSNN and the exact solution.}
\label{Fig:EX1}
\end{figure}

We then compare the present solution obtained by Chebyshev nodes (total $128$ training points) listed in Table~\ref{Table:exp1_node} with the numerical solution obtained by immersed interface method (IIM) \cite{Hu2015} which the latter is known to be second-order accurate for the elliptic interface problem Eq.~(\ref{Eq:elliptic}) on Cartesian grids.
Note that, in IIM, the total number of degree of freedom (number of unknowns), denoted by $N_{deg}$, is equal to the sum of the number of Cartesian grid points $m^2$ and the augmented projection foots on the interface, $m_\Gamma$, see \cite{Hu2015} for details.  Table~\ref{Table:exp1} shows the compared results where the IIM uses the grid resolutions
$m=m_\Gamma=128$ and $m=m_\Gamma=256$ so the number $N_{deg}=16512$ and $N_{deg}=65792$, respectively, while the number of parameters used in DCSNN are just $N_p=51$ and $N_p=101$. One can see that how significantly different those numbers of unknowns are.
With just a few number of neurons, $N=10$ and $20$, the solutions of the present network obtain one order of magnitude smaller than the IIM results.
Meanwhile, as expected, the increase of the number of neurons generally leads to better accuracy.

We should point out that the majority of the results in this paper is implemented in Matlab with double precision where the solution is denoted by $\phi_\mathcal{S}$.
We have also implemented the same network model to solve exactly the same problem in Python with single precision for which the solution is denoted by $\phi_p$.
As can be seen in Table~\ref{Table:exp1}, the accuracy of the solution is strongly limited by floating-point arithmetics.
For the ones implemented with single precision, the best accuracy in $L_\infty$ norm can be achieved in the order of $10^{-3}$ whereas the one with double precision can be as low as $10^{-7}$.

\begin{table}[h]
\centering
\begin{tabular}{c|c||c|cc||cc}
\hline
 $N_{deg}$ & $\|\phi_{IIM}-\phi\|_{\infty}$ & $(N,\, N_p)$ & $\|\phi_\mathcal{S}-\phi\|_{\infty}$ & $\|\phi_\mathcal{S}-\phi\|_2$ & $\|\phi_p-\phi\|_{\infty}$ & $\|\phi_p-\phi\|_2$ \\
\hline
16512& 7.719E$-$05  & (10,\,51)   & 3.005E$-$06 & 3.515E$-$07 & 1.258E$-$03 & 3.037E$-$04 \\
65792& 8.347E$-$06  & (20,\,101) & 2.490E$-$07 & 2.604E$-$08 & 1.108E$-$03 & 2.398E$-$04 \\
\hline
\end{tabular}
\caption{$\phi$: Exact solution. $\phi_{IIM}$: Solution obtained by IIM implemented in fortran with double precision. $N_{deg}=16512$ and $65792$ correspond to $m=m_\Gamma=128$ and $m=m_\Gamma=256$. $\phi_\mathcal{S}$: Solution obtained from DCSNN model implemented in Matlab with double precision.
$\phi_{p}$: Solution obtained from DCSNN model implemented in Python with single precision.}
\label{Table:exp1}
\end{table}

\paragraph{\textbf{Example 2}}

As the second example, we compare the results of DCSNN with the piecewise deep neural network proposed in \cite{he2020meshfree}, in which two (or multiple) individual neural nets are trained to approximate the function in each subdomain.
Here, the regular domain $\Omega = [-1,1]^2$ is separated by the interface that is given by a polar curve $r(\theta) = 1/2 + \sin(5\theta)/7$. We choose the exact solution as in \cite{he2020meshfree}
\begin{align*}
\phi(x_1,x_2) =
\left\{
\begin{array}{ll}
\exp(x_1^2+x_2^2) & \mbox{if\;\;} (x_1,x_2)\in\Omega^-,\\
0.1(x_1^2+x_2^2)^2-0.01\log(2\sqrt{x_1^2+x_2^2}) &  \mbox{if\;\;} (x_1,x_2)\in\Omega^+,\\
\end{array}\right.
\end{align*}
and set $\beta^- = 10$ and $\beta^+ = 1$. The present network is trained using $N = 50$ and $100$ neurons with randomly sampled training points $(M,M_b,M_\Gamma) = (400, 80, 80)$.
We measure the accuracy of solutions using the relative $L_2$ norm error and compare the results with piecewise deep neural net employing $4$ and $6$ hidden layers in \cite{he2020meshfree}, for which the same order of training data is used.
As one can see in Table~\ref{Table:exp2}, the present solution with only one hidden layer, and much less parameters, exhibits better accuracy.

\begin{table}[h]
\centering
\begin{tabular}{c|c||c|c}
\hline
 $(N,\,N_p)$ & $\|\phi_\mathcal{S}-\phi\|_2/\|\phi\|_2$ & $N_p$ & $\|\phi_\mathcal{DNN}-\phi\|_2/\|\phi\|_2$  \\
\hline
(50,\,251)   &  3.654E$-$04 & 25474 & 4.960E$-$03 \\
(100,\,501) &  3.185E$-$05 & 42114 & 3.727E$-$04 \\
\hline
\end{tabular}
\caption{The relative error in $L_2$ norm for the solution of DCSNN, $\phi_\mathcal{S}$, and for the solution of piecewise deep neural network~\cite{he2020meshfree}, $\phi_\mathcal{DNN}$.}
\label{Table:exp2}
\end{table}

\paragraph{\textbf{Example 3}}

This example aims to highlight the robustness of DCSNN to handle solving the elliptic interface problem (\ref{Eq:elliptic}) on an irregular domain.
Since the proposed network is a mesh-free method (i.e., not constrained by the locations of training points), the implementation is indeed straightforward. Different from previous examples, in this case the domain is set to be irregular and enclosed by the polar curve $r(\theta) = 1 - 0.3\cos(5\theta)$.
The embedded interface $\Gamma$ is also described by the polar curve, $r(\theta) = 0.4 - 0.2\cos(5\theta)$.
We use $20$ neurons in the hidden layer (thus $N_p=101$), and randomly sampled training points with $(M, M_b, M_\Gamma) = (64, 32, 32)$.
The result is shown in Fig.~\ref{Fig:EX3}.
We see that the solution can be accurately predicted by DCSNN without paying extra numerical efforts.
On the contrary, it can be difficult for traditional finite difference methods, such as IIM, to solve the problem on such irregular domain. Here, we emphasize that the irregular domain case can be properly handled in arbitrary dimensions without any substantial difficulty.

\begin{figure}[h]
\centering
\includegraphics[scale=0.38]{EX3.png}
\caption{Left: The DCSNN solution profile. Right: Error between DCSNN and the exact solutions. In this case $\|\phi_\mathcal{S}-\phi\|_\infty = 5.309\times10^{-6}$ and $\|\phi_\mathcal{S}-\phi\|_2=5.856\times10^{-7}$.}
\label{Fig:EX3}
\end{figure}

\paragraph{\textbf{Example 4}}

Next, we proceed to the  three-dimensional elliptic interface problem.
The interface is of an ellipsoidal shape, centered at origin with semi-principal axes of length $0.7$, $0.5$ and $0.3$, immersed in the regular cube $\Omega = [-1,1]^3$. As in Example~1, we compare the accuracy among three different training point distributions. The number of training points for this 3D problem is $(M,M_b,M_\Gamma) = (216,216,108)$ which is around 4 times of training points used in 2D case, while the number of neurons are set by $N=20, 30$ in the hidden layer. The results are shown in Table~\ref{Table:exp4_node}.
As expected, the Chebyshev nodes again gives the most accurate result compared to the other two results.

\begin{table}[h]
\centering
\begin{tabular}{@{}c@{\hspace{10pt}}c@{\hspace{10pt}}c@{\hspace{5pt}}c@{\hspace{10pt}}c@{\hspace{10pt}}c@{\hspace{5pt}}c@{\hspace{10pt}}c@{\hspace{10pt}}c@{\hspace{5pt}}}
\hline
\multirow{2}{*}[-3pt]{$(N, \,N_p)$} & \multicolumn{2}{c}{Chebyshev nodes} & & \multicolumn{2}{c}{uniform nodes} & & \multicolumn{2}{c}{random nodes}\\
\cmidrule(){2-3}\cmidrule(){5-6}\cmidrule(){8-9}
    & $\|\phi_\mathcal{S}-\phi\|_\infty$ & $\|\phi_\mathcal{S}-\phi\|_2$ & & $\|\phi_\mathcal{S}-\phi\|_\infty$ & $\|\phi_\mathcal{S}-\phi\|_2$ & & $\|\phi_\mathcal{S}-\phi\|_\infty$ & $\|\phi_\mathcal{S}-\phi\|_2$\\
\midrule
(20,\,121)   & 3.807E$-$05 & 4.102E$-$06 & & 3.244E$-$05 & 2.182E$-$06 & & 4.588E$-$04 & 2.093E$-$05 \\
(30,\,181) & 5.163E$-$07 & 5.666E$-$08 & & 3.789E$-$06 & 2.438E$-$07 & & 1.422E$-$05 & 1.546E$-$06 \\
\hline
\end{tabular}
\caption{The errors with different distributions of training data in 3D.}
\label{Table:exp4_node}
\end{table}

\begin{table}[h]
\centering
\begin{tabular}{c|c||c|cc||cc}
\hline
 $N_{deg}$ & $\|\phi_{IIM}-\phi\|_{\infty}$ & $(N,\, N_p)$ & $\|\phi_\mathcal{S}-\phi\|_{\infty}$ & $\|\phi_\mathcal{S}-\phi\|_2$ & $\|\phi_p-\phi\|_{\infty}$ & $\|\phi_p-\phi\|_2$ \\
 \hline
2201776   & 9.380E$-$04  &  (20,\,121) & 3.807E$-$05 & 4.102E$-$06  & 2.946E$-$03 & 4.676E$-$04 \\
17194216 & 2.890E$-$04  & (30,\,181)  & 5.163E$-$07 & 5.666E$-$08  & 1.590E$-$03 & 2.358E$-$04 \\
 \hline
\end{tabular}
\caption{$\phi$: exact solution. $\phi_{IIM}$: Solution obtained by IIM implemented in fortran with double precision.
$N_{deg}=2201776$ and $17194216$ correspond to $(m,m_\Gamma)=(128,104624)$ and $(m,m_\Gamma)=(256,417000)$.
$\phi_\mathcal{S}$: Solution obtained from DCSNN model implemented in Matlab with double precision.
$\phi_{p}$: Solution obtained from DCSNN model implemented in Python with single precision.
}
\label{Table:exp4}
\end{table}

We then compare the accuracy of the DCSNN solution with the 3D immersed interface solver proposed in \cite{Hsu2019}.
Note that, in 3D IIM, the total degree of freedom, $N_{deg}$, is now the sum of the number of Cartesian grid points $m^3$ and the augmented projection foots on the interface, $m_\Gamma$.
As shown in Table~\ref{Table:exp4}, the results obtained by the present model with double precision are more accurate than the ones by IIM, whereas the number of parameters of the network is significantly less than the one used in IIM.
Besides, the numerical solution implemented in Python with single precision  can achieve accuracy to the order of $10^{-3}$ in $L_\infty$ norm as well.

It is important to point out that, in DCSNN, the number of neurons at input layer scales as the dimension of the problem. So with the fixed number of neurons in hidden layer $N$, the total number of parameters $N_p$ increases linearly with the dimension $d$ (recall that $N_p=(d+3)N+1$).
On the contrary, the computational complexity is significantly increased in traditional numerical methods when the problem dimension increases.

\paragraph{\textbf{Example 5}}

 As the last example, we demonstrate the capability of DCSNN for solving high-dimensional elliptic interface problem (\ref{Eq:elliptic}) by taking the dimension size $d=6$.  For the problem setup,
we consider a $6$-sphere of radius $0.6$ as the domain $\Omega$ enclosing another smaller $6$-sphere of radius $0.5$ as the interface $\Gamma$.
The training points with $(M,M_b,M_\Gamma) = (100, 141, 141)$ are randomly sampled.
With the neuron numbers $N=10$, $30$ and $50$ (corresponding to total parameters $N_p = 91, 271$ and $451$), the network is trained with those training points.
The evolution of loss function and $L_\infty$  error against training step is shown in Fig.~\ref{Fig:EX5}.
We find that, an increase on the neuron number $N$ indeed results in a smaller mean squared error loss  (see panel (a)).
However, for all cases, the error attains a flat plateau in early training stage (within 100 iterations) and the descent of solution error becomes sluggish for proceeding training steps, see panel (b). Although not shown here,
our experiments show that adding more training points does not help increase the accuracy of predicted solution.
We attribute this slow convergence to the high dimensionality of the problem.
Similar observation was also found in deep Ritz method for solving high dimensional problems~\cite{weinan_2018}.
Despite that, our present solution for $N = 10$ still gives the training error $\|\phi_\mathcal{S}-\phi\|_\infty = 1.689\times10^{-4}$ which means the relative error can be controlled within $0.01\%$ even in higher dimensions.

\begin{figure}[h]
\centering
\includegraphics[scale=0.36]{EX5.pdf}
\caption{The evolution plots of (a) mean squared error loss, and (b) $L_\infty$ error.  $N = 10, 30$ and $50$.}
\label{Fig:EX5}
\end{figure}

\section{Conclusion and future work}

In this paper, a novel shallow neural network is constructed to approximate functions with jump discontinuities.
The crucial observation is that a $d$-dimensional piecewise continuous function can be augmented as a continuous function defined in $(d+1)$-dimensional space.
This function, based on universal approximation theory, can be approximated by a shallow, feedforward, fully-connected neural network.
We thereby propose a simple neural network architecture consists of an input layer of $(d+1)$-dimensional coordinate variable, a hidden layer with moderate number of neurons, and an output layer of the function itself.
We show that the present network is very efficient and accurate for piecewise continuous function approximation, and can be applied to solve as solution model for elliptic interface problems.
In particular, combining with a PINNs type loss function in solving elliptic interface problems, the present network output  approximates the solution with great accuracy and the result is completely competitive with the immersed interface method which is designed in particular for elliptic interface problems.
Furthermore, because of the mesh-free nature of the network, there is no difficulty to implement the network model to the problems on irregular domains or
 in high dimensions.

The present work, differs significantly from the ones existing in literature using DNN in a way that we consider only a completely shallow neural network (one hidden layer).
Nevertheless, to approximate functions or solutions that are highly oscillatory, one can simply increase the number of neurons in the hidden layer to achieve the desired accuracy. As we show in numerical experiments in this paper,
most of the testing problems can be solved with high accuracy by the present network with a moderate number (less than a hundred) of neurons. Notice that, a shallow network is much easier to train than the deep ones.

In the present work,  we only consider the stationary elliptic interface problems.
As a forthcoming extension, we shall consider time-dependent problems, and particularly the moving interface problems which will be left as future work.

\section*{Acknowledgement}

W.-F. Hu, T.-S. Lin and M.-C. Lai acknowledge supports by Ministry of Science and Technology,
Taiwan, under research grant 109-2115-M-008-014-MY2, 109-2115-M-009-006-MY2 and 107-2115-M-009-016-MY3, respectively.

\section*{References}

redpajama_set_name: RedPajamaArXiv


text:
Q: Search all fields in mySql I want to search all fields from  tables tblproduct in MySQL database a given string, possibly using syntax as:
SELECT * FROM tblproduct WHERE * LIKE '%textbox%'
Is it possible to do something like this?

A: Try this..
concate fields to search whole table
Select * from tblproduct  where Concat(field1, '', field2, '', fieldn) like "%textbox%"

or
Using MATCH and AGAINST in mysql
SELECT * FROM tblproduct  WHERE MATCH (field1, field2, field3) AGAINST ('textbox')

redpajama_set_name: RedPajamaStackExchange


text:
The VI Bolivarian Games (Spanish: Juegos Bolivarianos) were a multi-sport event held between August 22 - September 6, 1970, at the Estadio Olímpico del Complejo Polideportivo in Maracaibo, Venezuela. The Games were organized by the Bolivarian Sports Organization (ODEBO).

The Games were officially opened by Venezuelan president Rafael Caldera.  Torch lighter was javelin thrower José "Pachencho" Romero, who won the first gold medal ever in athletics for Venezuela at the 1947–48 Bolivarian Games.  The olympic stadium in Maracaibo was later named after him.  The athlete's oath was sworn by athlete Brígido Iriarte, who the gold medal in pentathlon at the 1951 Bolivarian Games.

A detailed history of the early editions of the Bolivarian Games between 1938 and 1989 was published in a book written (in Spanish) by José Gamarra Zorrilla, former president of the Bolivian Olympic Committee, and first president (1976-1982) of ODESUR.  Gold medal winners from Ecuador were published by the Comité Olímpico Ecuatoriano.

Participation
About 1122 Athletes from 6 countries were reported to participate:

Sports
The following 17 sports were explicitly mentioned:<ref
name=coe/>  For the first time, softball was included.  On the other hand, initially scheduled events in sailing, chess, and table tennis were cancelled.

Aquatic sports
 Diving ()
 Swimming ()
 Athletics ()
 Baseball ()
 Basketball ()
 Boxing ()
Cycling
 Road cycling ()
 Track cycling ()
 Equestrian ()
 Fencing ()
 Football ()
 Gymnastics (artistic) ()
 Judo ()
 Softball ()
 Shooting ()
 Tennis ()
 Volleyball ()
 Weightlifting ()
 Wrestling ()

Medal count
The medal count for these Games is tabulated below.  A slightly different number of medals (without Bolivia) was published elsewhere.  This table is sorted by the number of gold medals earned by each country.  The number of silver medals is taken into consideration next, and then the number of bronze medals.

References

Bolivarian Games
Bolivarian Games
Bolivarian Games
Bolivarian Games
B
Multi-sport events in Venezuela
Sports competitions in Maracaibo
20th century in Maracaibo
September 1970 sports events in South America
August 1970 sports events in South America

redpajama_set_name: RedPajamaWikipedia


Peter Collier, David Horowitz, "Anti Chomsky Reader"
This description is based on the MIT professor's writings on linguistics in the 1950s; but beginning with his criticism of the Vietnam War in the 1960s, Chomsky became much better known for his radical politics than for his theories of language. Over the past forty years he has gained a devoted following in the United States and Europe for his increasingly bitter–some say hysterical–censure of U.S. "crimes." Chomsky has complained about being ignored by mainstream publications such as the "New York Times," but in fact his steady stream of polemical works, like the best-selling "9-11," have made him the center of a veritable cult. In "The Anti-Chomsky Reader," editors Peter Collier and David Horowitz have assembled a set of essays that analyze Chomsky's intellectual career and the evolution of his anti-Americanism. The essays in this provocative book focus on subjects such as Chomsky's bizarre involvement with Holocaust revisionism, his apologies for Khmer Rouge tyrant Pol Pot, and his claim that America's policies in Latin America in the 1980s were comparable to Nazism. Scholar Paul Bogdanor writes about Chomsky's hatred of Israel. Ronald Radosh and David Horowitz discuss his gloating reaction to the September 11 attack. Linguists Paul Postal and Robert Levine reevaluate Chomsky's linguistics and find the same qualities there that others see in his politics: "a deep contempt for the truth, descents into incoherence, and verbal abuse of those who disagree with him." "The Anti-Chomsky Reader" presents a fascinating composite portrait of a man who arguably is our most influential public intellectual.


text:
// -*- mode:c++; tab-width:2; indent-tabs-mode:nil; c-basic-offset:2 -*-

#ifndef ZXING_MONOCHROMERECTANGLEDETECTOR_H
#define ZXING_MONOCHROMERECTANGLEDETECTOR_H

#include <vector>
#include <zxing/NotFoundException.h>
#include <zxing/ResultPoint.h>
#include <zxing/common/BitMatrix.h>
#include <QSharedPointer>
#include <zxing/ResultPoint.h>

namespace zxing {

struct TwoInts {
  int start;
  int end;
};

class MonochromeRectangleDetector  {
 private:
  static const int MAX_MODULES = 32;
  QSharedPointer<BitMatrix> image_;

 public:
  MonochromeRectangleDetector(QSharedPointer<BitMatrix> image) : image_(image) {  };

  std::vector<QSharedPointer<ResultPoint> > detect();

 private:
  QSharedPointer<ResultPoint> findCornerFromCenter(int centerX, int deltaX, int left, int right,
                                        int centerY, int deltaY, int top, int bottom, int maxWhiteRun);

  QSharedPointer<TwoInts> blackWhiteRange(int fixedDimension, int maxWhiteRun, int minDim, int maxDim,
                               bool horizontal);

  int max(int a, float b) { return (float) a > b ? a : (int) b;};
};

}

#endif // ZXING_MONOCHROMERECTANGLEDETECTOR_H


text:
Q: Why does java.lang.Cloneable not override the clone() method in java.lang.Object? The Java specification for the java.lang.Cloneable interface defines itself as signifying that any object that extends it also has implemented the clone() method that rests dormant within java.lang.Object. Specifically, it says that:

A class implements the Cloneable interface to indicate to the java.lang.Object#clone() method that it is legal for that method to make a field-for-field copy of instances of that class.

To me, this means that it should be assumed that every class that extends Cloneable therefore also has a public Object clone() method within it. This makes it easy to assume that the following is a valid method:
public static makeACloneFrom(Cloneable c)
{
  return c.clone();
}

however, this is not the case, as the entirety of the Cloneable source code (sans javadoc) is simply
package java.lang;

public interface Cloneable {
}

Which means that Cloneable#clone() does not exist (and trying to compile the example method above throws a compile-time error saying something like "cannot find symbol: method clone()"). Shouldn't the source code of Cloneable contain something to the effect of public Cloneable clone();?
Why aren't we allowed to assume that a class that implements Cloneable has a public Cloneable clone() method?

A: Because it's a poorly-designed interface.
From Effective Java (sorry, Google Books does not have a preview for the  2nd edition):

Item 11: Override clone judiciously
The Cloneable interface was intended as a mixin interface (Item
  18) for objects to advertise that they permit cloning. Unfortunately,
  it fails to serve this purpose. Its primary flaw is that it lacks a
  clone method, and Object's clone method is protected. You
  cannot, with resorting to reflection (Item 53), invoke the clone
  method on an object merely because it implements Cloneable. Even a
  reflective invocation may fail, as there is no guarantee that the
  object has an accessible clone method.

A: Ugh.  clone and Cloneable are broken, terribly designed, and shouldn't be used in new code.  (See Effective Java item 11.)
The reason for this particular thing is that Cloneable is a confusingly implemented, magical interface such that the mere act of implementing Cloneable changes the behavior of Object.clone with reflection.  Effective Java says:

...if a class implements Cloneable, Object's clone method returns a field-by-field copy of the object; otherwise it throws CloneNotSupportedException.  This is a highly atypical use of interfaces and not one to be emulated...