Optimal mean value estimates beyond Vinogradov's mean value theorem

We establish improved mean value estimates associated with the number of integer solutions of certain systems of diagonal equations, in some instances attaining the sharpest conjectured conclusions. This is the first occasion on which bounds of this quality have been attained for Diophantine systems not of Vinogradov type. As a consequence of this progress, whenever $u \ge 3v$ we obtain the Hasse principle for systems consisting of $v$ cubic and $u$ quadratic diagonal equations in $6v+4u+1$ variables, thus attaining the convexity barrier for this problem.Comment: Our original treatment of systems with degrees $k \ge 4$ contained a fatal flaw (thanks to S. T. Parsell for alerting us to this). The revised version gives an adapted treatment, leading to different results for $k \ge 4$. All results involving only quadratic and cubic equations remain unaffecte

Vinogradov systems with a slice off

Let $I_{s,k,r}(X)$ denote the number of integral solutions of the modified Vinogradov system of equations $$x_1^j+\ldots +x_s^j=y_1^j+\ldots +y_s^j\quad (\text{$1\le j\le k$, $j\ne r$}),$$ with $1\le x_i,y_i\le X$ $(1\le i\le s)$. By exploiting sharp estimates for an auxiliary mean value, we obtain bounds for $I_{s,k,r}(X)$ for $1\le r\le k-1$. In particular, when $s,k\in \mathbb N$ satisfy $k\ge 3$ and $1\le s\le (k^2-1)/2$, we establish the essentially diagonal behaviour $I_{s,k,1}(X)\ll X^{s+\epsilon}$.Comment: 19 page

Phase Transitions in Generalised Spin-Boson (Dicke) Models

We consider a class of generalised single mode Dicke Hamiltonians with arbitrary boson coupling in the pseudo-spin $x$-$z$ plane. We find exact solutions in the thermodynamic, large-spin limit as a function of the coupling angle, which allows us to continuously move between the simple dephasing and the original Dicke Hamiltonians. Only in the latter case (orthogonal static and fluctuating couplings), does the parity-symmetry induced quantum phase transition occur.Comment: 6 pages, 5 figue

Warhogs: A History of War Profits in America

The Puritans condemned war profiteering as a Provoking Evil, George Washington feared that it would ruin the Revolution, and Franklin D. Roosevelt promised many times that he would never permit the rise of another crop of war millionaires. Yet on every occasion that American soldiers and sailors served and sacrificed in the field and on the sea, other Americans cheerfully enhanced their personal wealth by exploiting every opportunity that wartime circumstances presented. In Warhogs, Stuart D. Brandes masterfully blends intellectual, economic, and military history into a fascinating discussion of a great moral question for generations of Americans: Can some individuals rightly profit during wartime while others sacrifice their lives to protect the nation? Drawing upon a wealth of manuscript sources, newspapers, contemporary periodicals, government reports, and other relevant literature, Brandes traces how each generation in financing its wars has endeavored to assemble resources equitably, to define the ethical questions of economic mobilization, and to manage economic sacrifice responsibly. He defines profiteering to include such topics as price gouging, quality degradation, trading with the enemy, plunder, and fraud, in order to examine the different guises of war profits and the degree to which they have existed from one era to the next. This far-reaching discussion moves beyond a linear narrative of the financial schemes that have shaped this nation\u27s capacity to make war to an in-depth analysis of American thought and culture. Those scholars, students, and general readers interested in the interaction of legislative, economic, social, and technological events with the military establishment will find no other study that so thoroughly surveys the story of war profits in America. Stuart D. Brandes is professor of history at the University of Wisconsin-Rock County. Stuart D. Brandes has written a solid, thoroughly researched, and exceedingly unemotional and restrained history of a neglected subject, carrying it through World War II with a limited consideration of the Cold War. . . . [H]is book is not to be ignored by either economic or military historians. —American Historical Review Offers a treasure of information on greed and selfishness during crises in America. —Reviews in American History A valuable addition to the historiography of the United States munitions industry and its relationship to American democracy and capitalism. —Journal of Southwest Georgia History The only comprehensive attempt to deal with the many facets of government contracting during time of military crisis through World War II. . . . This balanced account is must reading for anyone interested in American military history. —Military History of the West Stuart D. Brandes is the first scholar to tackle the complex and ever-shifting issue of war profits across nearly the entire scope of American history. This highly readable narrative asks the right questions and supplies cogent, well-reasoned answers based on impressive research and careful reflection. —Daniel E. Sutherlandhttps://uknowledge.uky.edu/upk_united_states_history/1106/thumbnail.jp

Non-equilibrium correlations and entanglement in a semiconductor hybrid circuit-QED system

We present a theoretical study of a hybrid circuit-QED system composed of two semiconducting charge-qubits confined in a microwave resonator. The qubits are defined in terms of the charge states of two spatially separated double quantum dots (DQDs) which are coupled to the same photon mode in the microwave resonator. We analyze a transport setup where each DQD is attached to electronic reservoirs and biased out-of-equilibrium by a large voltage, and study how electron transport across each DQD is modified by the coupling to the common resonator. In particular, we show that the inelastic current through each DQD reflects an indirect qubit-qubit interaction mediated by off-resonant photons in the microwave resonator. As a result of this interaction, both charge qubits stay entangled in the steady (dissipative) state. Finite shot noise cross-correlations between currents across distant DQDs are another manifestation of this nontrivial steady-state entanglement.Comment: Final versio

Fully-dynamic Approximation of Betweenness Centrality

Betweenness is a well-known centrality measure that ranks the nodes of a network according to their participation in shortest paths. Since an exact computation is prohibitive in large networks, several approximation algorithms have been proposed. Besides that, recent years have seen the publication of dynamic algorithms for efficient recomputation of betweenness in evolving networks. In previous work we proposed the first semi-dynamic algorithms that recompute an approximation of betweenness in connected graphs after batches of edge insertions. In this paper we propose the first fully-dynamic approximation algorithms (for weighted and unweighted undirected graphs that need not to be connected) with a provable guarantee on the maximum approximation error. The transfer to fully-dynamic and disconnected graphs implies additional algorithmic problems that could be of independent interest. In particular, we propose a new upper bound on the vertex diameter for weighted undirected graphs. For both weighted and unweighted graphs, we also propose the first fully-dynamic algorithms that keep track of such upper bound. In addition, we extend our former algorithm for semi-dynamic BFS to batches of both edge insertions and deletions. Using approximation, our algorithms are the first to make in-memory computation of betweenness in fully-dynamic networks with millions of edges feasible. Our experiments show that they can achieve substantial speedups compared to recomputation, up to several orders of magnitude