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China's Strategic Vision, Strengths, and Vulnerabilities
Kevin Rudd's Address at the West Point Senior Conference
The following is ASPI President Kevin Rudd's full address to the 55th West Point Senior Conference.
It's good to be back at West Point. I was here 12 months ago addressing your cadets on Xi Jinping's worldview. And then six months ago I went to the U.S. Naval Academy at Annapolis to talk about America's strategic response.
For Americans, West Point speaks to so many of the great events of American history—from the birth of the Republic, the horrors of the CivilWar through to the roll-call of many of the great military commanders of recent history—Grant, Pershing, Patton, MacArthur, and Eisenhower. For an Australian, this academy speaks to the ties that bind our two proud, robust, in-your-face democracies and the deep shared history of our two militaries since we first went into battle, together, on the Western Front 100 years ago on July 4, 1918—and in every major international conflict since.
The world of 1918 is a vastly different world to that of 2019, although its deep resonances continue to this day. After decisively shifting the balance of forces in favor of the Allies in WWI, America after the Paris Peace Conference withdrew into its strategic shell for a generation. And the world was a worse place for it. After Pearl Harbor, America was once again fundamental to a final Allied victory. But this time, rather than retreat, America crafted the post-war international order, reinforced by the power of its military in all corners of the world, and a doctrine of containment that took it through nearly half a century of Cold War that eventually saw the collapse of its strategic nemesis the Soviet Union. But that was 30 years ago. The central question today in the minds of America's friends and foes alike is whether the United States will retain the political resolve and strategic capacity to underpin the global order of the future. Or will there be an emerging sense of strategic vacuum, within which its adversaries begin to move and where its allies begin to hedge against a different future. Ultimately, this is America's decision, and America's alone. But the consequences are global.
The year 1919 has a different significance in Chinese historiography. Chinese political leaders and diplomats, following the dispatch of hundreds of thousands of Chinese construction workers to the Western Front at America's request to support the Allies, had been assured by President Wilson that following the Paris Peace Conference, Germany's colonies in China would be returned to Chinese sovereignty. Indeed, Wilson's Fourteen Points were heralded as a beacon of hope for the fledgling Chinese Republic as Chinese nationalists, socialists, and communists alike hailed him as a savior of the Chinese nation following three-quarters of a century of Western colonial occupation. Even a young Mao Zedong was captured, at least for a moment, by Wilson's magic. But when Wilson capitulated at the conference, surrendering Germany's Chinese territories to Japan instead, America, in the eyes of Chinese political elites of both the left and right, became responsible for the great betrayal. The peace conference gave rise to what is called in China the "May Fourth Movement" when Peking University students took to the streets, radicalizing China's politics and entrenching a deep Chinese historical narrative that neither the West nor the United States could ever be trusted again with China's future.
The May FourthMovement, whose centennial will be commemorated next month across the Chinese speaking world, also gave rise to the birth of the Chinese Communist Party (CPC) just two years later. America and theWest have been demonized in Communist Party propaganda ever since, drawing on skillfully intertwined ideological and nationalist reasons. First, because the United States and the West are bastions of liberal democracy and capitalism which still stand fundamentally opposed to the Marxist-Leninist orthodoxy of the CPC. Second, because theWest carved China up and America did little, if anything, to help. And now a third, that the United States and the West will do everything possible to contain China's 21st-century rise. These have become the enduring internal narratives on the Chinese Communist Party.
Xi Jinping will lead national celebrations for the centennial of the Communist Party in 2021. This will be a major national event, not least because this anniversary is one of the twin pillars of Xi's self-proclaimed "China Dream" of China reclaiming global great power status; with the second pillar being the centennial of the establishment of the People's Republic itself in 2049, by which time China's national transformation is to be completed. Again, the core political narrative of the Party will be that only through its leadership has China finally been delivered the national wealth and power dreamed of by previous generations of reformers, and this has been achieved despite the United States and the West, not because of their help, support, or engagement.
History matters in the U.S.-China relationship. Both in what actually happened, what it led to, and the series of causes and effects that follow. But equally important is the perceived historiography of each side, and their established national narratives of the relationship, because past perceptions, be they factually accurate or not, also shape future behaviors.
Trajectories for the Indo-Pacific Region
This conference is not about China's rise, U.S.-China relations, or China's future in the global order. I've been asked to address future strategic trends in the Indo-Pacific region. But the truth is, I find it impossible to see the region's future other than through the principal lens of the U.S.-China relationship. Other dynamics are of course at play within the wider region. But how the security and economic future of the region will be materially changed because of the increasingly competitive and confrontational relationship between the United States and China; and how third countries begin to perceive, predict, and then anticipate through their actions the longer-term outcome of this new era of strategic competition, are overwhelming all other factors.
This matters now not just for the region, but for the world. This is because of the emerging centrality of the Indo-Pacific to the future of the global economy, trade, investment, capital flows, technology, innovation, and supply chains. It's also because of the growth of military expenditures by the states of the Indo-Pacific beyond that of all other regions. Just as it is this region where we see the major drivers and consequences of climate change at work with the potential for major population displacements. As well as the enduring hazards of strategic geography, geopolitics, and energy supply routes, reinforced by an abundance of unresolved territorial disputes that directly engage the region's great powers. However comforting or distressing it may be to our European friends, the reality is that against virtually all measures, the center of global strategic gravity has now shifted to the Indo-Pacific region. This is dramatically demonstrated with the following data points.
- In 2009, Europe and North America accounted for 45% of global GDP, while Asia contributed 37%. Today the figures are reversed, with Europe and North America contributing 38% and Asia 46%. The IMF predicts that this gap will only widen.
- In 1990, the share of trade between Western markets was almost 60% of total world trade. Today it is 30%. At the same time, trade between emerging markets was a miserly 6% in 1990, while now it stands at almost 30%.
- China is now the second largest recipient of foreign direct investment behind the United States. Recent reforms regarding foreign ownership of Chinese banks, brokerages, and insurance firms are likely to accelerate foreign direct investment over the coming years.
- Patent applications are surging in China; in 2017 they increased by 14% from the prior year alone. Regionally, 65% of the world's patents registered in 2017 were in Asia, a 15% greater share than 10 years prior.
- In 2000, Asia accounted for 25% of the world's research and development expenditure; in 2015 it climbed to 40%. China alone is responsible for almost one-third of the global increase in R&D spending.
- This changing economic center of gravity to the Indo-Pacific is also reflected in the generation of greenhouse gas emissions. In 1990, Asia represented 25% of global GHGs, while now that figure is 49%. Today, the top three global emitters are China, the United States, and India at 28%, 15%, and 7%, respectively.
- Across the Indo-Pacific, military expenditure has not only matched rising economic growth, it has outstripped it. China's declared military expenditure has leapt from USD $68 billion in 2007 to $228 billion in 2017. This is about 35% of U.S. defense expenditure, measured at $656 billion in 2017. However, in terms of growth over that span, U.S. military expenditure grew by 5%, while China's grew 230%. India's expenditure grew 165%.
All this has occurred in a region with unresolved territorial conflicts between North and South Korea and the United States; Japan and Russia over the Northern Territories; Japan and China over Senkaku/Diaoyu; China and the United States over Taiwan; multiple states over the South China Sea; the Sino-Indian border; India and Pakistan over Kashmir; as well as the growing debate over China's expanding number of naval bases across the Indian Ocean. It is therefore the great Indo-Pacific Paradox— characterized by rapid economic growth and growing levels of economic integration, despite a deep underlying strategic instability and relatively weak pan-regional institutions, all tempered by the emerging mega-challenge of climate change.
The China Dynamic
China is the new, great driving dynamic in the wider Indo-Pacific region, where few countries are not impacted by China's growing economic and strategic footprint. We see this across all economic indicators as a natural product of China's size, its increasingly assertive diplomacy, and growing naval presence. Much is made in the international commentary on the ambitions of China's Belt and Road Initiative (BRI). But the reality is that the China factor is being felt much more acutely through a multiplicity of separate bilateral engagements across the region that largely go unreported, where regional governments all wrestle with opportunities and challenges of dealing with a resurgent China.
In part, this reflects China's continuing grand strategy over several decades. In part, however, it reflects the new dynamics of Xi Jinping's leadership. To recap on what I said here last year about Xi Jinping's worldview, I define this through seven concentric circles of interests, the core of which is the absolute centrality of keeping the Party in power. This is followed by:
- maintaining national unity;
- ensuring sustainable economic growth while preserving environmental sustainability;
- cultivating benign and ultimately compliant relationships with China's 14 bordering states;
- securing China's continental periphery by projecting its economic and geostrategic influence across the Eurasian continent;
- projecting its maritime power across East Asia, the western Pacific, and the Indian Ocean; avoiding armed conflict with the United States while decoupling, over time, America's network of Asian alliances;
- optimizing good relations with the developing world—across Asia, Africa, and Latin America—thereby enhancing China's position across the range of global institutions; and
- reforming the institutions of global governance over time, toward aligning their practices, personnel, and institutional culture more closely to Chinese interests and values.
China's Strengths
China's grand strategy has many strengths, although it also has significant weaknesses which seem to find much less space in the breathless global commentary we see on China's inexorable rise. Among China's strengths, perhaps its greatest is the consistency of its strategy, since Deng's return to the leadership of China 40 years ago, to make China wealthy and powerful though domestic market-based reforms encouraging private incentive, and then unleashing these entrepreneurs on the international market. But China also carefully tracks changes in the international political and economic environments and makes tactical adjustments whenever it judges necessary. They did so after the global reaction to Tiananmen in 1989. They did so again in response to the Asian and later Global Financial Crises. Just as they are doing again in response to the recent slowing in their domestic economic growth rates, as well as some international push-back to its BRI juggernaut. China's strategy is constant, yet always remains remarkably tactically agile. This is a great strength.
China's leadership also understands that its continuing political legitimacy in the eyes of the Chinese people rests with the economy. The leadership have always intervened by fiscal, monetary, or administrative means to sustain growth at around 6% because this is what they have internally judged to be the threshold necessary to sustain social stability. The Party tracks social discontent by multiple means and responds with a range of carrots and sticks. But whenever living standards and employment are at risk, the Party actively intervenes. To the great frustration of China's hardy team of liberal economic reformers, long-term structural reforms are regularly sidelined if the country's macro-political circumstances warrant it. The Party, after all, is determined to survive.
A further strength for the regime is the formidable resources of China's internal security apparatus. China's domestic security services have more personnel than the entire People's Liberation Army (PLA). Their effectiveness has also been turbocharged by the new surveillance technologies they have acquired or developed to keep the citizenry under control. China is governed not just by a Marxist party; it is also a Leninist party that understands full well what it means to obtain and sustain political power by all means—including violent means if necessary. China's leadership undertook a 10 year-long intensive study on the collapse of the Soviet Union and have no intention of allowing anything similar in China. China, as we have seen on a number of occasions, has few qualms in deploying force where necessary to guarantee Party control.
Fourth, China has achieved remarkable success in transforming its indigenous culture of technological innovation. China's leadership recognized this as a strategic weakness back in 2013. They embarked on a large-scale national turn-around strategy driven by a combination of state research institutions, some leading-edge state-owned enterprises (SOEs), and an increasingly rampant Chinese private tech sector. Xi Jinping has recognized the new technology industries as fundamental to China's future global economic and military competitiveness. And in artificial intelligence, he has seen it as a possible means of leapfrogging the United States.
Finally, China's additional strength has been the continuing absence of an American grand strategy of its own in the post-Soviet era. China's leadership have observed over many decades the passing parade of U.S. presidents, but until recently have not detected any fundamental change in American policy toward it. While China has been surprised by the U.S.-China trade war initiated by President Trump, they are confident it will soon find its resolution. And while they are vigilant in seeking to identify evidence of deep changes in other domains of U.S. strategic behaviors toward them, for China, the jury is still well and truly out.
Indeed, sometimes I think China is more brutally accurate than its American and international counterparts in its analysis and understanding of real as opposed to ephemeral change, both here in the United States as well as globally. Perhaps it's a deep intellectual training in Marxist dialectics that causes China's leaders to separate out what's in the headlines in the West, as opposed to what constitutes deep underlying structural trends. China, for example, despite the trade war, still publicly defines the current period as one of great strategic opportunity for the country's continued rise. Furthermore, when the Chinese observe the state of relations between the United States and its European, as well as select Asian allies—the gradual dismemberment of the European Union, the growing
fragmentation of Western politics including the growing polarization between the far left and the far right—their analysis becomes more optimistic again. And on China's central preoccupation with the future of its economy, China couldn't believe its luck when they saw the United States trashing the Trans-Pacific Partnership (TPP), and the absence of an American alternative to the BRI, not to mention America's inability to hold even its allies in check on their joining the Asian Infrastructure Investment Bank (AIIB). And now, it seems, in America's allies not complying with its requested ban of Huawei's 5G technology in their domestic communications networks. So as Beijing sees it, things are not going badly at all.
China's Challenges
China, however, also has many challenges of its own, often invisible to the Western eye, but which remain the daily concerns of its leaders. In many essential respects, these concerns represent the flip side of the various strengths I enumerated. First, Xi Jinping may have had remarkable success in consolidating his own personal leadership position. Nonetheless, China has a long history of instability at the time of leadership transition. This was most spectacularly evident after the death of Mao. We saw it again in the events of 1987–89. But there were also significant rumblings in 1992 when Deng intervened to secure the leadership of new Party Secretary Jiang Zemin. Then, during the most recent leadership transition to Xi Jinping, Bo Xilai was a contender before being imprisoned for corruption—with political convulsions ensuing across the country, resulting in the purge of a number of senior Party leaders who had been allies of Bo.
There are also divided views within China on the wisdom of Xi Jinping having abolished term limits at the 19th Party Congress for the position of President. It had been generally assumed that if Xi Jinping wanted to remain inactive office by the time of the 20th party congress in 2023, he would be allowed to do so, although possibly in a position other than President. However Xi's decision to change the constitutional limits on high office, as well as his high-profile initiatives on island reclamation in the South China Sea, the 2025 industry strategy championing China's high tech future, and on the Belt and Road have caused some of his critics within the Party to accuse him of having gone too far. These critics further argue that this "overreach" has unnecessarily and prematurely provoked reaction from the United States and others across the West. This has not been a critique of Xi Jinping's grand strategy to make China wealthy and powerful and to reclaim its position as a global great power. Rather, it is a critique that by abandoning Deng Xiaoping's policy of "hide your strength, bide your time, never take the lead" that Xi Jinping has made a significant tactical error by attracting international opposition much earlier than was necessary.
On the economy, Xi also faces a number of deep challenges. These have in large part been caused by his own deep convictions about the future role of the Party in the economy. By instinct and ideological conviction, Xi is a party loyalist. For those reasons, when he became Party General Secretary in 2012, he concluded that he needed to act decisively to prevent the continuing decline of the Party as the country's core institution of political power. He initiated the anti-corruption campaign. He strengthened the Party's hold over ideological rectitude across the country. He cracked down on political, academic, and religious dissent. And he has reasserted the role of the Party within the operations of the Chinese private sector.
This, however, has resulted in a negative reaction from China's rising entrepreneurial class. During the course of 2018, the Chinese private sector began an investment strike because of their increasing objections to many tenets of the government's financial and economic policy. These objections focused on Xi Jinping's support for SOEs over private firms; his reported concern about private firms becoming too big, or at least bigger than the Party; his imposition of strict foreign exchange controls, constricting the ability of private firms to operate comfortably internationally; the skewing of the tightening of monetary policy, causing banks to withdraw lines of credit from a number of private sector firms while favoring SOEs in the rationing of credit; as well as Party secretaries within private firms having an increasingly substantive role in the company's operations, in contrast to their somewhat nominal position in the past.
The net result of all of the above, well before the impact of the U.S.-China trade war was felt, was a slowing of Chinese economic growth throughout the course of 2018 until policy leaders in Beijing began to react decisively in the last quarter. Fiscal and monetary policy loosening followed, together with a number of policy statements by Xi and others aimed at rebuilding private sector confidence in the future. Nonetheless, with the private economy now representing 60% of Chinese GDP, Xi Jinping faces a continuing structural challenge to balance his natural instincts favoring Party control, with an increasingly restive private sector which increasingly resents its economic future being muzzled by a reimposition of Party orthodoxies from the past.
A third new problem presenting itself to China's leadership is the emergence of a structural current account deficit. China's current account surplus only a decade ago stood at 10% of GDP. It now stands at 0.4% of GDP. The decline in China's traditional surplus has been generated by increased Chinese imports, the declining international competitiveness of certain Chinese exports (because of improving wage rates within the country), together with Chinese consumers having finally decided that high savings rates aren't the only way to plan for the future; and that foreign goods and services have their own intrinsic attractions. China having to fund a current account deficit for the first time represents the underlying reason why Beijing, in the course of the last 12 months, has embraced a series of policy changes liberalizing its own financial services industry. China has indicated that there will be new openings for foreign capital in Chinese equity markets, bond markets, as well as the development of its futures market. Announcements have also been made allowing more than 51% foreign equity in Chinese banks, insurance companies, and brokerage firms. These are large changes. They're not driven by a desire to appease foreigners. They're driven by the growing need to attract foreign capital in order to rebalance the current account. Of course, once this opening to international capital markets occurs, it is very difficult to close the window. Indeed, if China does become structurally dependent on the net inflow of foreign capital, then it follows that foreign capital can also choose to leave the country if and when it begins to doubt the fundamental market orientation of Chinese economic policy. In other words, if the Party turns further "left" on economic policy in the future, there would be a flight of foreign capital, under which circumstances China could conceivably face a current account crisis. This, therefore, represents a significant long-term challenge for Chinese leaders seeking to balance the competing political and economic imperatives.
A further challenge for Xi Jinping also lies on the economic front with China's double deficit dilemma. Public sector indebtedness has been fueled by local government debt over more than a decade. Indeed when aggregated, China's national debt (albeit primarily domestically denominated) now runs at some 280% of GDP. China's monetary policy authorities have put in place some corrective action on this score and the numbers have started to slowly come down. But there is still a long way to go. However, it is China's budget deficit which arguably represents the larger long-term challenge for the authorities. China's budget dilemma is also worsened each time the Chinese leadership reach for the fiscal lever to restimulate their economy to keep growth levels up. Furthermore, demographic change in China is seeing the rapid aging of the population which the abolition of the one-child policy has failed to turn around. All this means that China faces a deep budgetary challenge in dealing with growing health, elderly care, and social security costs for its population. Proper public provision in these domains will also be essential for the preservation of long-term stability. But the more that domestic budget pressures are felt in these areas, the more that constraints will emerge for the Chinese government in making large-scale expenditure decisions in other areas, including on its military.
On the international front, China has also encountered resistance to the rollout of major policies such as the Belt and Road Initiative. The election of Mahathir Mohamad as Prime Minister of Malaysia provides a large case in point. There has been resistance in Sri Lanka too, witnessed by their public reaction to handing over to China a port facility built with Chinese capital after Sri Lanka could no longer service the debt on the Chinese government loan. Even among loyal allies such as Pakistan, there has been local political reaction to Chinese-funded infrastructure projects through the BRI. Furthermore, given the potentially enormous financial dimensions of the BRI, Chinese financial institutions have quietly indicated to the Party that they themselves have limitations in terms of how much they can fund of infrastructure projects across the more than 60 countries that have expressed interest in the BRI in some form. This is particularly the case when many of these projects are unlikely to generate a financial or even economic rate of return for a very long time, if at all. As further evidence of its tactical agility, China has now decided that the best way forward is to increasingly internationalize the BRI in order to diversify the sources of investment. It may also seek to scale back its scope. China has recently gone into global listening mode on the future of the BRI. The initiative will continue, but its operationalization may be tempered into the future.
Finally, on the domestic front, there remain a number of local aspirations and tensions, each of which is capable of boiling over in the future. Environmental concerns lead the way. While significant improvements have been made in reducing air pollution in China's major cities, this is not uniformly the case across the country. And impact of urban air pollution has already begun to have an effect on respiratory diseases, cancer rates, and urban life expectancy. The inadequacy of China's healthcare facilities for the general public is also a source of continuing social and political tension across the country. Just as we also find the Party's reaction to rising religious sentiment (including Protestant Christianity, Buddhism, and Islam in the case of Xinjiang) is itself generating ground level dissatisfaction across the country. China remains officially Marxist and atheist. Xi Jinping has repeatedly emphasized this fact throughout his term. Crackdowns against Islam in Xinjiang, and in many Chinese provinces against unauthorized church construction and religious activity, reflects the Party's concern about different sources of ideational authority emerging across the country. For these reasons, domestic political criticism arising from grassroots social concerns represents a continuing challenge to the Party's long-term hold on power.
Relations with Russia
Nonetheless, when China contemplates its aggregate national balance sheet of assets and liabilities, what Beijing still sees, with some justification, is a cup half full. One additional geopolitical trend also working in China's favor over some decades now has been the normalization of Sino-Russian relations. The depth of the Sino-Soviet conflict of the 1960s, 70s, and 80s cannot be underestimated. However, the resolution of the Sino-Soviet border in 1989 between Deng Xiaoping and Mikhail Gorbachev and the subsequent collapse of the Soviet Union brought about a fundamental change in China's overall strategic posture toward its Russian neighbor. Not only did Sino-Russian relations begin normalizing in the 1990s, once Vladimir Putin returned to the Russian presidency in 2000, the pace of engagement between Russia and China began to intensify further. This accelerated again under Xi Jinping. Indeed, the intensity and the intimacy of the relationship between Putin and Xi should not be underestimated. The evidence would suggest that we are beginning to see the emergence of a de facto military alliance between China and the Russian Federation, despite official denials to the contrary.
Beijing and Moscow have virtually identical positions on all major global political issues. Their foreign policies are well coordinated at the UN Security Council. There is an effectively agreed upon protocol between them that Russia follows China's lead on the Asia-Pacific, whereas China follows Russia's lead in the Euro-Atlantic region and the Middle East. Furthermore, the intensity of military exercises between the two countries has increased. Combined naval exercises as far away as the Mediterranean and the Baltic suggest that something of structural significance is unfolding in the relationship. Of course, there have been frustrations, not least over China's failure to meet deep Russian expectations to fill the financial gap left by the imposition of Western financial sanctions following the Russian invasion of Ukraine in 2014. Nonetheless, the conclusion in Moscow has been that China represents Russia's only alternative. And it would be profoundly wrong for Western analysts to conclude this deep shift in the Moscow-Beijing relationship is only temporary. It is beginning to evidence all of the characteristics of a mutually convenient, long-term arrangement.
Regional Responses
When we look beyond China itself to the wider Indo-Pacific region, from Beijing's perspective we also see a series of relatively benign responses to China's rise in general, as well as to the particular dynamics of the unfolding strategic competition emerging between China and the United States.
On the Korean Peninsula, China is now in a stronger position than it was with both the Koreas only a year or so ago. The tumultuous year following President Trump's decision to directly engage Kim Jong-un has also had a profound effect on China-North Korea relations. Trump's North Korean diplomacy has resulted in the unfreezing of Beijing-Pyongyang relations which had been in deep freeze for over five years. Prior to Trump's new diplomacy toward Kim Jong-un, Xi Jinping's attitude to "Kim the Younger" bordered on absolute contempt. But if it was good enough for Trump to meet with Kim without conditions attached, it was also good enough for Xi. And so began a much deeper reconciliation between China and North Korea than has so far occurred with the United States. China will never compromise its strategic relationship with the North by forcing the North to denuclearize. That's because abiding Chinese strategic doctrine is predicated on maintaining a benign strategic buffer between China and South Korea, Japan, and the American forces based there.
As for South Korea, the danger of President Trump's North Korea policy is that it has created political expectations in the South for some sort of accommodation with the North, even if the North refuses to denuclearize. While refusal to denuclearize is anathema to U.S. policy, that is not necessarily the case in the South under the current center-left government in Seoul. Indeed, given that the North is highly unlikely to denuclearize, it's possible to see a scenario unfolding in which the South begins to drift away from America's strategic orbit as Seoul looks for its own accommodation with the North, assisted by China. China does not want to see a united Korea on its doorstep, let alone one which is firmly within America's embrace. We should not forget that this was what caused China to enter the Korean War in 1950. And now through its own diplomacy nearly three-quarters of a century later, China seeks to bring about benign relations with both North and South Korea as both become progressively more dependent on the Chinese economy and as the South is steadily coaxed away from the United States. This should not come as a surprise given that it has long been China's declared strategy to see an end to all U.S. alliances in Asia. The unknown political variable in all this is what will happen with center-right political sentiment in South Korea once it finally reorganizes itself after a long series of corruption scandals, and whether they will fundamentally oppose any significant distancing of the South from America. The bottom line is that President Trump's North Korean diplomacy has unleashed new dynamics in the triangular relationship between Beijing, Pyongyang, and Seoul which not only have an uncertain trajectory but potentially have a landing point inimical to long-term American and allied interests.
As for Japan, Prime Minister Abe continues to defy the history books on the political durability of his Liberal Democratic Party (LDP) administration. The center-left opposition remains in disarray. At one level, Japan remains one of the strongest continuing pillars of American allied interests in Asia. That is also likely to continue under any successor to Abe in the LDP leadership. Japanese foreign and defense policy has also become more activist and assertive under Abe's leadership. Japan led the rehabilitation of the TPP following the Trump administration's decision to leave by holding together the "TPP 11" states in an ambitious regional free trade agreement while still excluding China. Abe has also concluded a major free trade agreement with the European Union where many European states have been under pressure from the BRI and a range of other Chinese trade and investment initiatives. Japan has also led the establishment of a USD $200 billion Partnership for Quality Infrastructure, in cooperation with the Asian Development Bank, which to date represents the only sizeable alternative to the BRI for the countries of Southeast and South Asia. And in 2017, Japan joined with India in promoting the Asia-Africa Growth Corridor in direct response to China's Maritime Silk Road Initiative. As for defense policy, Abe has led successful efforts to reinterpret Article 9 of Japan's post-war pacifist constitution to enable the Japanese Self-Defense Forces (SDF) to operate in more expansive military exercises and operations in the future—both independently and with the U.S. and other allies.
Nonetheless, it would be naive to conclude that Japan has placed all its eggs in a single strategic basket. Abe's important visit to Beijing in October 2018, after a seven years effective freeze in the Japan-China relationship triggered by Japan's decision in 2011 to "nationalize" Senkaku/Diaoyu, indicates that Tokyo has also begun to hedge its future strategic bets. Chinese military activity around the disputed islands has significantly reduced, as have Japanese SDF deployments in response. Abe also opened the door to future Japanese collaboration on BRI projects having earlier signaled the possibility of joining China's AIIB if Japanese environmental and transparency concerns could be addressed. Furthermore, Japan appears to be mindful of the limitations facing the future of the Quadrilateral Security Dialogue (the Quad) with the U.S., Indian, and Australian navies given India's on-again, off-again approach to full participation. Japan would, therefore, seem to be weighing its own strategic future as it assesses the long-term trajectory of U.S. policy under Trump and his successors on the strength and reliability of America's future security commitments to its allies.
I've written elsewhere that Southeast Asia has become the new "great game" in strategic competition between China and the United States and its allies. China's overwhelming economic presence in these smaller economies has created a series of political and foreign policy opportunities for China from the Philippines, to Brunei, to Myanmar. China has also succeeded in quarantining the management of its territorial claims and land reclamation efforts in the South China Sea to a regional diplomatic process. This is designed to negotiate, over time, a "code of conduct" to manage conflicting interests in the region. Even states with a traditionally more skeptical approach to China, such as Singapore, Vietnam, and Indonesia, appear to be hedging their bets on the future as well, seeking to balance their relations between Beijing and Washington. There is also a growing political perception across ASEAN that President Trump does not recognize the strategic importance of the region, irrespective of what other branches of the administration may be doing, particularly through the State Department, and the Pentagon and the Indo-Pacific Command.
That does not mean that the region has become plain sailing for China. As I mentioned earlier, the election of Malaysian Prime Minister Mahathir last year, in a campaign warning against the dangers of his country and others falling into a long-term Chinese debt trap, has sent ripples across the wider region. There are also significant infrastructure projects, including most recently sensitive port infrastructure in Indonesia, that have been awarded by Jakarta to Indian and Japanese bids over the Chinese. Furthermore, ugly racial reactions against the growing presence of ethnic Chinese in Southeast Asia is once again stirring ancient prejudices. Nonetheless, my overall argument here is that Southeast Asia remains very much in play in this new "great game," although the United States must recognize the fact that the sheer weight of the Chinese economic footprint, in the absence of an effective American alternative, would tend to favor Beijing as the winner over the medium to long term.
India is in the middle of national elections where polling indicates a relatively close outcome. Prime Minister Narendra Modi's Hindu nationalist party over the last five years has moved India toward a closer strategic relationship with the United States than any of Modi's predecessors. In the perhaps unlikely event that the opposition Congress Party and its coalition partners wins the election, it is an open question how much a new Prime Minister Gandhi would then seek to unravel what Modi has achieved in the U.S. relationship. The 2018 bilateral agreement on enhanced military, intelligence, and defense acquisition cooperation represents a major milestone in the security relationship. Bilateral military exercises with the United States, as well as trilateral exercises with the United States and Japan, have increased in frequency, although India has repeatedly balked at these expanding further to include Australia through the Quad. The strengthening of the U.S.-India relationship has been driven by a rising China; repeated major incidents along the disputed Sino-Indian border; a continuing toxic relationship with Pakistan, which has long been supported by China; as well as the construction of Chinese naval and civilian port facilities across the Indian Ocean from Bangladesh to Sri Lanka, to Pakistan through to Tanzania, Sudan, and Djibouti.
India is nonetheless dissatisfied with its economic relationship with the United States given the Trump administration's decision to strip India of its preferential tariff status in selling Indian goods into the American market. Furthermore, India's determination to continue to source various defense purchases from Russia creates a further obstacle in the evolution of the overall strategic relationship with the United States, particularly as these can trigger automatic sanctions under U.S. legislation. Finally, it's important to note that as with Japan's Abe, Modi has also sought to hedge his ultimate strategic bets with the United States and China through his own far-reaching bilateral summit with Xi Jinping in Wuhan in April 2018, and the "strategic guidance" both sides then issued to their respective militaries to better manage tensions along the border. Xi and Modi have met on four occasions since then and have publicly reported that there continues to be improvement in the bilateral relationship based on their rolling review of the framework agreed to at Wuhan. Once again, India is being cautious about its strategic future, including long-term U.S. policies, posture, and capabilities in the Indian Ocean.
This brings us finally to the Gulf. China's core interest in the Gulf is to secure its long term energy supplies of oil and gas. More recently, however, China has initiated joint investments between Chinese sovereign funds together with their Saudi and Emirati counterparts in third country projects where China wants to mitigate its own financial risk. China would like Saudi Arabia, in particular, to participate in BRI projects, perhaps even turning Saudi Arabia into the BRI gateway to Africa. Mohammed bin Salman's (MBS) visit to China in February 2019 was an important turning point in the relationship, given Saudi Arabia's increasing international isolation following the Jamal Khashoggi assassination. China's official media waxed lyrical following the MBS visit, not only on the significance of the Kingdom's new "look east" policy and its implications for the BRI but also in providing Saudi Arabia with fresh opportunities to diversify its future strategic relationships beyond an unreliable America.
Once again, however, one swallow doth not a summer make. Both Saudi and the United Arab Emirates remain deeply skeptical concerning Beijing's much older and closer economic and military relationship with Iran, which Riyadh and Abu Dhabi have long identified as their fundamental strategic threat in the Gulf. This skepticism is compounded by China's close strategic relationship with Russia, which has stood opposed to Saudi interests in the resolution of the Syrian conflict. And to this should be added growing concerns in the wider Muslim world over Chinese policies toward their own Muslim minority in Xinjiang. Nonetheless, the Gulf, for the first time, also now appears to be in play for China in a way that would have been unimaginable only a decade ago. Gulf governments, like governments across the region, are increasingly torn between the economic potential of their burgeoning relationship with China and the security dilemmas this creates for their relationships with Washington and Tehran. Importantly, American political leaders also seem to have overlooked the fact that as they have celebrated the end of American energy dependence on the Gulf through the development of the U.S. domestic fracking industry, it has been China that has filled the demand gap in taking Gulf oil and natural gas contracts. China has now become the Gulf states' largest energy market. And the pan-regional reality is that economic interests, over time, have a significant impact on political and foreign policy considerations, and security policy decision-making as well. Of this, Chinese decision makers are acutely aware.
Nothing is ever predetermined in national or international politics. Political agency means that ultimately governments decide on what futures they want for their countries. And they then prosecute strategies, successful or otherwise, to give their aspirations practical effect. There are, however, deep structural forces also at work in international relations that over time begin to set the parameters for the freedom to maneuver for any individual state. History informs us that the most powerful of these parameters is economic. And it is here that we begin to contemplate the unfolding asymmetry of the U.S.-China relationship, both regionally and globally.
Across the coming decade, most analysts conclude that China is likely to become a larger economy than the United States using either purchasing parity pricing or market exchange rates. At the same time, the United States is likely to remain the dominant global and regional military power through until mid-century and possibly beyond. Ultimately, however, the history of national militaries is that they eventually yield to national economic realities. The current gravitational pull of the Chinese economy is unprecedented in modern economic history. We've seen this for some years in trade flows where China has already been the world's largest trading power for the last few years. We are beginning to see a similar trend in foreign direct investment flows around the world. Capital flows, innovation, and technology potentially stand poised to complete the picture.
The success or failure of Xi Jinping's dream, both at home and abroad, ultimately rests on the economy. And as the preceding analysis has suggested, there are many things that can still go wrong with China's fundamental economic policy settings and associated environmental constraints. Of these, however, arguably the most significant is the as yet unresolved question within China on the long-term trajectory of its domestic political economy. The essence being: will the Chinese Communist Party continue to tolerate the next generation of market reforms for its economy, thereby enabling China to burst through the middle-income trap in order to realize Xi Jinping's dream? Or will the Party balk at this challenge because it fears that by doing so it creates an increasingly dominant private sector, outcompeting China's state-owned enterprises, and thereby creating a powerful private entrepreneurial class whose policy influence ultimately renders the Party politically redundant? In many respects, we had a trial run on this question after the 2015 Communist Party plenum, as the Party progressively abandoned its 2013 economic reform blueprint in the name of economic, social, and political stability. Although in recent months, slowing growth, combined with other structural forces at play within the Chinese economy, may have caused a policy to rethink at the highest level of the Party and state. Reform of China's financial markets seems to point in that direction. But as for the rest of the economic reform agenda, the picture remains unclear.
As for the United States, I have not been asked to address U.S. strategy or its operational policy in the Indo-Pacific region. I, therefore, do not intend to comment further, other than to observe that if China has developed a consistent grand strategy over several decades, it is important that the United States starts to think and act in similar terms. I've read carefully the U.S. National Security Strategy of December 2017 and the National Defense Strategy of January 2018. I also understand that further work is currently underway in the U.S. interagency process. But I've yet to see substantive evidence of a whole-of-administration, let alone whole-of-economy or whole-of-nation strategy to deal with the challenges of the future. Some argue that this is not possible in elected democracies. It's certainly true that democracies are less tidy than authoritarian states. But this does not of itself preclude the possibility of a fully integrated national strategy, with sufficient bipartisan buy-in, that would command American policy and action into the future.


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Technology changes SO fast! Our new Melrose Area Public School App has been updated. There are now more choices for Push Notifications, be sure to check which ones apply to you! This app will be used to notify parents about school closings, and other important updates. Please reach out to an administrator or secretary at school if you have any questions about our app. READ MORE >
Listen to news and updates from Mr. Winter! READ MORE >
Winter Storm Weather Announcements will be broadcast over the following radio and television stations:Radio StationsKASM 1150 am AlbanyKEYL 1400 am Long PrairieKCLD 104.7 FM St. CloudKIK 100.7 FM AlexandriaWCCO 830 am MinneapolisTelevision StationsWCCO Channel 4KSTP Channel 5KMSP Channel 9KARE Channel 11School Closing CriteriaClosing school due to poor weather... READ MORE >
Minnesota Community Education was established in 1969 - celebrating 50 years of service! Community Education serves 336 districts in Minnesota, and many more throughout the United States. What Is Community Education? Community Education is an opportunity for local citizens and community schools, agencies and institutions to become active partners in addressing... READ MORE >
The first Band Concert of the 2019-20 school year is Thursday, November 21 at 8 p.m. in the Marit Elliott Performing Arts Center. The concert will feature Christmas songs and a variety of other music. The Jazz Band will also be performing. Cost is $4 for students and $6 for adults, or you may use your Activity Pass. Come and enjoy the musical talents of 7-12 grade... READ MORE >
Starting this January, Melrose Middle School needs 2 math tutors to give their time and talent to help our kids improve their math skills. Maybe you are a stay-at-home parent or retiree, recent grad or career changer – you could be a great tutor. No experience? No problem – we'll train you. You don't even have to be great at math.There are perks (even beyond... READ MORE >
If you have children in Melrose Area Public Schools, you should get our App! Search the App Store for Melrose Area Public Schools MN. The district will be using the App to share news and notifications about school closings, and updates for parents. The App is not just for parents, though, it's a great tool to stay up-to-date on news, events, and information about... READ MORE >
Congratulations to the Middle School Students of the Month in October! Math - Ramona Lurken-Tvrdik and Christopher Herrera FACS - Brooke Klaphake Industrial Tech - Trevor Blonigen and Brandon Dragseth Science - Daniel Mueller and Turner Beuning English - Kaylee Ellering and Camryn Roering Music - Yoselin Ambriz Ramirez and Anna Neu Art - Cecilia Sjogren PE... READ MORE >
Congratulations to the following high school students for 1st quarter, who were recognized by their teachers for their academic efforts. Way to go! Art: Ebelin Botello Music: Katrinna Deters Phy Ed: Jayden Danzl Spanish: Alexis Wensmann German: Erika Doetkott Social Studies: Ellie Heller English: Madalyn Kraemer Science: Tyler Pohlmann Math: ... READ MORE >
Today was our Pep Rally Day to kick off our Boosterthon! We gathered together to learn about how to help our school and our brand new character theme. It's going to be a TON of fun! Plus, we are kicking everything off today with a challenge called the My First Pledge Challenge! We want to see how many students can get registered on funrun.com TONIGHT and ask... READ MORE >
Melrose Preschool is fortunate to have Reading Corps Tutor, Laura Bertram, on staff. Minnesota Reading Corps tutors are trained using the science of how children learn to read — and then they work on boosting literacy skills. It's a nearly impossible for teachers to deliver individualized instruction to every student. But because that's all Reading Corps... READ MORE >
Picture retakes for Melrose Area Elementary are on Tuesday, October 29th. READ MORE >
Would you like to make an impact in the lives of children? Become a Foster Grandparent Program classroom volunteer! Adults can benefit by interacting with the playful, imaginative minds of youth. Working with kids can teach us more about ourselves, inspire our own creativity, and ground us as we grow older.For more information, please call or email Pat Scherf, FGP... READ MORE >
K-12 will continue with tradition and be doing the Jingle Jar this year. The dates are October 29-31. We are asking students and staff to give any amount they can spare. Check the couch cushions!The Women of Today will purchase gifts for families in need over the holiday season with the money raised. Some donations will be left at school to help with student... READ MORE >
Melrose School picture retake day will be next Tuesday, October 29th. All students should have received their pictures - if they have not, please have them stop by the office. READ MORE >
Our 2019 Fall Musical is "Once Upon a Mattress." Show dates are November 7, 8, 9 at 7:30 p.m. and November 10 at 2 p.m. in the Marit Elliott Performing Arts Center. All tickets are reserved and can be purchased at Melrose High School or Melrose locations of CMCU and Freeport State Bank. READ MORE >
Radio Interview 10/16 READ MORE >
Welcome to our new website! A few tips for finding what you need - you can use the MENU for a dropdown of our site pages, or you can use the SEARCH box to look for specific information. If you still need help, feel free to contact Holly Berscheit (email@example.com), Tammy Oliver (firstname.lastname@example.com) or Stacey Austing-Jacobson (firstname.lastname@example.com) for... READ MORE >
Homework Help has started!! Grades 1-5.....Tuesday and Thursday in the Elementary Library from 3:00 - 4:00 pm...Students must have a form turned in to attend....Forms are in the Elementary office Grades 6-12....Monday and Wednesday in the Middle School WIN room from 3:00 - 4:30 pm. No forms necessary students need to sign in and out. If you have any questions about... READ MORE >
Congratulations to the Middle School Students of the Month in SeptemberMath - Ian Baysinger and Noah Hellmann-MaderFACS - Isaac Frericks and Macie BauerIndustrial Tech - Wyatt MalchowScience - Sierra Austin and Olivia Van BeckEnglish - Jada Rausch and Amelia BrowerMusic - Meadow Schaefer and Jessica PohlmannArt - Hayley Ettel and Alyssa StordahlPE - Ria Nelson and... READ MORE >
Mr. Winter does a monthly radio interview at KASM, listen to what he has to share! https://5il.co/aezm READ MORE >

subset: commoncrawl


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Thanks for the invite Data Grillen, See You Next Year
Everyone you atteeded Data Grillen 2019, thanks so much for the invite this year. I had a great time visiting with everyone, both those that I knew from prior years and those that I met for the first time this year. Hopefully I'll get the chance to see everyone again next year. Look for an...
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I travel a lot. But occasionally I get asked "Why". The answer to that is pretty simple and comes down to three simple things. 1. When I just out of high school (18 years old ish) I had no clue what I'd be doing for a living. My first real job out of high school was working Tech Support at an...
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New Delhi, Fe 20: In addition to the hardcore diplomatic issues including terror which would figure prominently at the talks between Indian and Saudi sides on Wednesday, issues of Haj quota and imprisonment of Indians in Saudi Arabia will also figure prominently.
According to official sources here on the issue of demand for enhanced quota for Haj, the government of India has given some documents to the Saudi side to deliberate and decide.
"....As you know, on this there is a process where they will look into certain indicators and documents and then decide whether quota can be increased. And we have presented certain documents to them and we will have to wait for the outcome. This is something which will be raised at the talks," the source said.
As of now, India has a quota of 1.75 lakh Haj pilgrims from India but lately about three lakh people have applied and hence India is trying to enhance the quota.
Breaking protocol, Prime Minister Narendra Modi on Tuesday evening received the Saudi Crown Prince Mohammed bin Salman bin Abdulaziz Al-Saud as the latter arrived on his two-day crucial and maiden state visit to India.
The visit is happening at a time when there is heightened tension between India and Pakistan following the Pulwama terror attack by Pakistan-based Jaish-e-Mohammad (JeM). Saudi Foreign Minister Adel al-Jubeir has said his country will be keen to try to de-escalate tensions between the two countries.
Sources also said issues pertaining to imprisonment of Indians in Saudi jails will also be taken up.
"We will take up this issue also. This is something we are aware of. We have consular issues and other things which we will definitely like to enhance. In fact, we have taken this up before as well," the source said.
In fact, there are different 'sets of people' from India in Saudi jails including hardened criminals and people involved in petty crimes and hence this is an important issue to be raised, sources said.
In a tweet on Tuesday evening, MEA spokesman Raveesh Kumar said: "A new chapter in bilateral relations. Breaking protocol, PM Narendra Modi personally receives Prince Mohammed bin Salman bin Abdulaziz Al-Saud, Crown Prince of Saudi Arabia as he arrives on his first bilateral visit to India".
Meanwhile, answering questions related to possibility of Indian investment in Saudi Arabia, a senior official said: "India is actively encouraging Indian industries to go there".
With regard energy sector, the official pointed out that in 2016 Joint Statement itself it was pointed out that - both sides should try to "transform the buyer-seller relationship in the energy-sector to one of deeper partnership focusing on investment and joint ventures in petrochemical complexes, and cooperation in joint exploration in India, Saudi Arabia and also in third countries".
The two sides have also agreed over the months to focus on areas of training and human resources development and cooperation in research and development in the energy sector.
In this regard, the two sides expressed the need for regular meetings under the umbrella of India-Saudi Arabia Ministerial Energy Dialogue, the official said.


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Posted On: 08/17/18 6:45 PM
Brock Henry is willing to be patient. The athletic 6-foot-4 combo guard from Southridge High School fought through injury in the summer to play his best ball at the end of the summer. Now that he's no longer traveling, Henry has some time off to reflect on his summer of AAU ball and give an update on his college recruitment status.
"Things went well in July," Henry said. "I think I ended the AAU season on a good note in Vegas and things are starting to pick up a little as far as recruiting goes. A few more colleges are starting to contact me and show interest."
Henry noted that Lewis & Clark, Lewis-Clark State, and Clark College have been the ones most in contact since the summer ended. "They've been saying that they're interested and they'd love to have me visit," Henry said. "I'm not sure if they're close to offering but fingers crossed."
With that said, Henry is keeping all of his options open. He's taking a little bit of time off and then it will be time for his senior season – one in which he feels the Skyhawks will make some noise.
"I'm feeling really good about this upcoming season for us," Henry said. "I know we lost a lot of key guys but I think we still have the potential to be one of the top teams in Oregon and I think we'll end up surprising a lot of people."
Henry currently ranks as the #40 player in the PrepHoops Oregon Class of 2019 Rankings.


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Connie from Fairfield Age: 30. Looking for a nice man for body and soul.
He was a little too big for the invisibility cloak now. He was still as solid as dragonskin. Harry's hand fell to Hermione's waist as he pulled her closer to his side. he wanted to feel her juicy thighs brush against his as then went to wherever she had in mind. But they didn't care this time. Part 1 " costars did indeed ditch their tops and lube up in silver paint for a "full-on," steamy snogging session in the new PGrated film. Rescue in the Rain
Louise from Fairfield Age: 30. Hot and attractive, daring and energetic girl will invite a man who appreciates beauty, charm and a sense of tact.
Boy And His Cloak
After the first take, he was like, 'Whoa, there. Daniel Radcliffe just can't keep his clothes on. So was it weird for Watson to swap spit with Radcliffe, whom she's known for 10 years and has frequently said is like a brother to her. It was two in the morning on a freezing night in December and the boy's dormitory in Gryffindor tower was alive with snoring and heavy breathing.
Phyllis from Fairfield Age: 35. My dream is to find a man able to bring to orgasm. Love the new feel. I love sex.
Susana from Fairfield Age: 32. Looking for a man who is willing to spend time not only in bed.
Stella from Fairfield Age: 35. I am gentle, affectionate,kind,well-groomed, with a good figure and no less beautiful soul.
She got back up, put and put the book on the armchair, nobody would be awake to find it for another five hours at least, 'not here,' she whispered to Harry as she eyed the girls' dormitory door again. Hermione took out the phial with green liquid and drunk it like a shot of alcohol, Harry did the same with the blue concoction she had made for him. The fire flickered a comforting orange light across the carpet and up the walls onto the ceiling, facing the fire on a red armchair was Hermione Granger, she had a book on her lap that only Harry had saw her with. If you don't think one scene is enough, don't worry -- Yates has more than one scene in mind. I was so desperate to get it over. It was so hard for either of them to do this without slipping out of the invisibility cloak. the cloak was making everything so incredibly hard. They both looked around cautiously, and then locked eyes with each other when they concluded they were the only two people in the library.
Katie from Fairfield Age: 21. Looking for an experienced man, hope for a passionate night)


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Like a mountain bike, a Moun10Bike Geocoin yearns to roll to new, exciting destinations. Feel free to place it in a geocache, or pass it on to a friend and see where it goes!
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Tips for passing driving theory test You're about to embark on a journey of learning to drive and it is time to consider preparing for your theory test. Although arguably less stressful than the practical test, the pressure of needing to pass the theory test beforehand can be worrying. Here at Arrow Driving Academy, we
Tag: driving instructors yorkshire
Happy New Year from Arrow! Happy New Year and all the best for 2016 from the Arrow Driving Academy team. We would like to take this opportunity to post a huge thank you to all of the dedicated individuals who take part in our adventure as a new and ambitious driving academy in Hull. A
What a great year! Arrow Driving Academy Hull are proud to say that 2015 was a successful one and we will be welcoming in 2016 with a bang! This year we have expanded our business significantly, growing to a fantastic 16 driving instructors. It really is hard to believe that just over two years
New and improved driving test; This year there have been a number of proposals to improve the UK driving test. The overall drive for these proposals has been the incentive to ensure that drivers are well-prepared and therefore more likely to pass their test first time. Major changes to the UK driving test are set
Important news update from the DVLA The Driving and Vehicle Licensing Agency have recently sent out a warning to the public in accordance with a recent scam that has been floating around the UK. This scam involves false emails reaching random people and claiming to be the DVLA. The email asks you to provide your
Changes to Driving Test Manoeuvres New UK driving test; This year the DVSA have announced that they are beginning tests for a whole new driving test routine. According to news headlines across the UK, this is the biggest driving test shakeup in 20 years. From April 2015 the DVSA will be trialling their new proposed
The expiry of paper driving licenses; As of 8 June 2015, the paper element of UK driving licenses will be invalid and no longer issued by the DVLA. This is the paper counterpart to the photo card driving license. The paper counterpart exists as it displays information about your personal driving categories and any endorsements
Driving lessons in Beverley Arrow Driving Academy offers first class driving lessons in Beverley and the Beverley area. If you or anyone you know would like the opportunity to learn to drive with one East Yorkshires premier driving schools then please let us know and we will be back in touch asap. We have spoken
Arrow is on the lookout for ADIs Arrow Driving Academy is looking for Approved Driving Instructors to join our franchise. Currently we are based in Hull and offer driving lessons in East Yorkshire. With an emphasis on quality and friendliness we are a driving school that knows the value of positive feedback from our customers.
Driving lesson deals in Hull and East Yorkshire Arrow Driving Academy is a driving school based in Hull and East Yorkshire. We offer driving lessons, free online theory training and the 5 lessons for £55 deal. So that is the full lessons 1hr each of driver training for only £55. Which is fantastic value and


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Deriving the information entropy of the multivariate gaussian
- Introduction and Trace Tricks
- Derivation
Introduction and Trace Tricks
The pdf of a multivariate gaussian is as follows:
, where
is the covariance matrix, which can be expressed in vector notation as
. I might make the derivation of this formula its own post at some point, but it is in Strang's intro to linear algebra text so I will hold off. Instead, this post derives the entropy of the multivariate gaussian, which is equal to:
Part of the reason why I do this is because the second part of the derivation involves a "trace trick" that I want to remember how to use for the future. The key to the "trace trick" is to recognize that a matrix (slash set of multiplied matrices) is 1x1, and that the value of any such matrix is, by definition, equal to its trace. This then allows you to invoke the quasi-commutative property of the trace:
to push around the matrices however you desire until they become something tidy/useful. The whole thing feels rather devious to me, personally.
Beginning with the definition of entropy
substituting in the probability function for the multivariate gaussian in only its second occurence in the formula,
We will now consider these two terms separately.
First term
First, we concern ourselves with the first ln term:
since all the terms other than form a constant,
and because is a PDF, it integrates to 1. Thus, this component of the equation is
Second term (Trace Trick Coming!)
Now we consider the second ln term
because is a 1 x N matrix, is a N x N matrix, and is a N x 1 matrix, the matrix product is a 1 x 1 matrix. Further, because the trace of any 1 x 1 matrix , we can conclude that the 1 x 1 matrix .
As such, our term becomes
, which, by the quasi-commutativity property of the trace function, ,
. Because is a scalar and the natural logarithm and exponentials may cancel, the properties of the trace function allow us to push the and the integral inside of the trace, so
But, $\int p(x)(x-\mu)(x-\mu)^{T}dx=\Sigma$ is just the definition of the covariance matrix! As such,
Recombining the terms
Bringing the above terms back together, we have
as desired.