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Let $\Omega \subset {{\mathbb {R}}}^{n+1}$, $n\geq 2$, be an open set with Ahlfors regular boundary that satisfies the corkscrew condition. We consider a uniformly elliptic operator $L$ in divergence form associated with a matrix $A$ with real, merely bounded and possibly nonsymmetric coefficients, which are also locally Lipschitz and satisfy suitable Carleson type estimates. In this paper we show that if $L^*$ is the operator in divergence form associated with the transpose matrix of $A$, then $\partial \Omega $ is uniformly $n$-rectifiable if and only if every bounded solution of $Lu=0$ and every bounded solution of $L^*v=0$ in $\Omega $ is $\varepsilon $-approximable if and only if every bounded solution of $Lu=0$ and every bounded solution of $L^*v=0$ in $\Omega $ satisfies a suitable square-function Carleson measure estimate. Moreover, we obtain two additional criteria for uniform rectifiability. One is given in terms of the so-called “$S

This chapter examines theories that explain the causes of war. It considers ideas advanced by political scientists, sociologists, biologists, and philosophers, showing that different explanations of war give rise to different requirements or conditions for peace. After highlighting the difficulties in studying war, the chapter discusses human nature explanations of war, citing such factors as frustration, misperception, misunderstanding, miscalculation, and errors of judgement as well as the role of human collectives including factions, tribes, nations, and states. It then describes the bargaining model of war before turning to inter-state wars, intra-state conflicts, and ethnic conflicts. It also explores the debate over whether ‘greed’ or ‘grievance’ are the main causes of civil wars. The chapter concludes that identifying a single cause appropriate to all wars is an exercise in futility and that a worldwide ‘just’ peace is unattainable.

Military power is the legally sanctioned instrument of violence which governments use in their relations with each other, and in an internal-security role. Japan is sometimes cited as the new model of how materialistic, growth-orientated states can achieve prosperity without military strength. The problem of reconciling or striking a balance between the need to concentrate military power in the hands of a few and the need to preserve democratic values is a fundamental one for any democratic state. The political control of the military is almost taken for granted in the United Kingdom where there is a long tradition of political neutrality in the armed services, and where the threat of military rule is quite unreal. Many of the critics of military power have emphasised the uselessness of weapons of mass destruction for all practical purposes. The declining utility of military power in its traditional functions may reflect the manifestly diminished interest which western states have in foreign affairs generally..

From a Western viewpoint, the Soviet armed forces have been the looming ogre in the Cold War drama. The military policy which has directed their powerful muscles has often seemed a mystery. Soviet leaders, like their Tsarist predecessors, have never been confident about their state’s security from external threat. Since 1945 Soviet strategic policy has been dominated by the need to meet the requirements of deterrence and defence against the dominant United States enemy, there have been some other important threats to Soviet security. In addition to reacting to these strictly “defensive” problems Soviet military strength has also been used in a variety of ways to support the advancement of foreign policy. Knowledge about the processes by which defence policy has been formulated in the Soviet Union has always been limited. However, over a twenty-year perspective two trends have been perceptible: decision-making today is more bureaucratic than in Stalin’s time, and in some senses military “influence” has increased..

‘Strategy’ is a deadly business. It is concerned with the darker side of human nature, in that it examines the way in which military power is used by governments in the pursuit of their interests. Strategists talk of ‘taking out’ cities, of making ‘counterforce’ strikes with ‘collateral damage’, of crossing ‘thresholds’, and of engaging in tactical nuclear ‘exchanges’. In democratic societies few would wish to challenge either the supremacy of political direction or the view that strategic analysis should concentrate on identifying and evaluating the various choices’ available to states in their use of military power for ends clearly defined by political authorities. Perhaps the most pervasive assumptions underlying contemporary strategy are those which are associated with the theory of political behaviour known as ‘realism’. Most of the realists’ ideas have been absorbed, either consciously or unconsciously, by contemporary strategic thinkers.

This series provides a selection of articles from the past. In Fifty years ago: Productivity, morale and occupational medicine John Garnett briefly explores the problems of the 20th century workplace, including stress, boredom, and lack of motivation.

This chapter examines theories that explain the causes of war. It considers ideas advanced by political scientists, sociologists, biologists and philosophers, showing that different explanations of war give rise to different requirements or conditions for peace. After highlighting the difficulties in studying war, the chapter discusses human nature explanations of war, citing such factors as frustration, misperception, misunderstanding, miscalculation, and errors of judgement as well as the role of human collectives including factions, tribes, nations and states. It then describes the bargaining model of war before turning to inter-state wars, intra-state conflicts, and ethnic conflicts. It also explores the debate over whether ‘greed’ or ‘grievance’ are the main causes of civil wars. The chapter concludes that identifying a single cause appropriate to all wars is an exercise in futility and that a worldwide ‘just’ peace is unattainable.

Speakers: 1. Vasilis Chousionis (University of Helsinki, Finland) Square functions and uniform rectifiability 2. Leonardo Colzani (Universita degli Studi di Milano, Italy) Localization and convergence of Fourier series and integrals 3. Javier Duoandikoetxea (Universidad del Pais Vasco/Euskal Herriko Unibertsitatea, Spain) A comparison of the characterizations of A∞ 4. Bruno Franchi (Universita degli Studi di Bologna, Italy) Differential forms in Heisenberg groups and div-curl systems 5. Gustavo Garrigos (Universidad de Murcia, Spain) Maximal functions, weights and convergence to initial data of certain Poisson equations 6. Jose Maŕia Martell (ICMAT, Universidad Autonoma de Madrid, Spain) The Dirichlet problem for elliptic systems in the upper-half space 7. Alessio Martini (Christian-Albrechts-Universitat zu Kiel, Germany) Hypoelliptic operators and sharp multiplier theorems 8. Joan Mateu (Universitat Autonoma de Barcelona, Spain) Euler equation and vortex patches 9. Carlos Perez (Universidad de Sevilla, Spain) Around a conjecture of E. Sawyer for the Hilbert Transform and weights 10. Ezequiel Rela (Universidad de Sevilla, Spain) Optimality of weighted estimates without examples

Purpose Mevalonate pathway inhibitors are potentially useful chemotherapeutic agents showing growth inhibition and pro-apoptotic effects in cancer cells. The effects of statins and bisphosphonates on cancer growth are attributed to a reduction in protein isoprenylation. Post-translational modification and activation of GTPase binding Ras superfamily permit the recruitment of these signal proteins to membranes where they mediate the cancer phenotype. Here, the effects of three inhibitors of the mevalonate pathway and one specific inhibitor of sterol regulatory element-binding proteins were studied in both an ER-negative, Ras-inactive breast (MDA-MB-231) and lung adenocarcinoma (CaLu-1) cells in vitro. Methods Treated cells were subject to genome-wide gene expression profiling. A gene subset was established so that the epithelial to mesenchymal transition (EMT) could be observed and compared with signalling protein shifts. Results Within the subset, some genes normally up-regulated during EMT were asymmetrically reduced by a Δ-24 DHCR inhibitor in the lung cells. Signalling proteins associated with caveolae were down-regulated by this oxidoreductase inhibitor, while those associated with membrane rafts were up-regulated. Conclusions This study decouples isoprenylation effects from cholesterol events per se. The data support a hypothesis that caveolae are abolished by Δ-24 DHCR intervention and it is revealed that these microdomains are vital EMT signalling structures for lung cells but not ER- and Ras-negative breast cells. When signalling by extracellular signals is quenched by removal of the hydrophilic conduit provided by caveolae, the transcriptome responds by moving the cellular identity towards quiescence. Electronic supplementary material The online version of this article (doi:10.1007/s00432-015-2074-3) contains supplementary material, which is available to authorized users.

In this study, blown films were produced from three different high density polyethylene (HDPE) resins. Further, these blown films were oriented along the machine direction using either traditional machine direction orientation (MDO) or compression roll drawing (CRD MDO) technology. The stretched/oriented films were compared for their water vapor transport and optical properties as a function of the extent of orientation (i.e., draw ratio, DR). In addition to that, these properties were directly compared between the oriented and unoriented (blown) films of the same thickness. The present study revealed that the water vapor transmission rate (WVTR) as a function of draw ratio (DR) went through a maxima. Detailed morphological characterization showed that initially, at low DR, stretching resulted in lamellar organization (along the MD). Consequently, the tortuosity in the diffusion path decreased and the overall WVTR increased. However, beyond a critical DR, lamellar crystals transformed to microfibrillar crystals. During this process the amorphous content of the HDPE chains decreased and geometric redistribution of the amorphous phase occurred along with some orientation. As a combination of all these effects, the WVTR was found to decrease beyond the critical DR. Unlike transport properties, optical properties monotonically improved as a function of DR. Further, for both, the barrier and optical properties, the absolute values were found to be a strong function of the resin physical properties. Finally, compression roll drawing technology (CRD MDO) utilizes a patented process that simultaneously applies a stretching and compressive force to orient polymer chains homogeneously without any tiger striping (uneven deformation). Consequently, CRD MDO stretched samples showed a lower surface roughness compared to their traditional MDO stretched counterpart. Therefore, for the same resin and DR, CRD MDO stretched samples displayed markedly better barrier properties and optics, especially lower total haze and higher gloss.

This work is devoted to image restoration (denoising and deblurring) by variational models. As in our prior work [Inverse Probl. Imaging, 3 (2009), pp. 43--68], the image $\tilde f$ to be restored is assumed to be the sum of a cartoon component $u$ (a function of bounded variation) and a texture component $v$ (an oscillatory function in a Sobolev space with negative degree of differentiability). In order to separate noise from texture in a blurred noisy textured image, we need to collect some information that helps distinguish noise, especially Gaussian noise, from texture. We know that homogeneous Sobolev spaces of negative differentiability help capture oscillations in images very well; however, these spaces do not directly provide clear distinction between texture and noise, which is also highly oscillatory, especially when the blurring effect is noticeable. Here, we propose a new method for distinguishing noise from texture by considering a family of Sobolev norms corresponding to noise and texture. I...

There is increasing evidence that statin treatment can be beneficial in certain cancer patients. To determine if these benefits are a direct result of the cholesterol-lowering effects of statins or a result of secondary, protein transcription effects, the impacts of pravastatin and a cholesterol sequestrating agent methyl-beta-cyclodextrin (MbetaCD) on mRNA expression in the breast cancer cell MDA-MB-231 and the lung carcinoma cell Calu-1 have been compared by microarray techniques. The effects of these agents on cholesterol-rich rafts and caveolae, which have significance in cancer signaling, have also been examined. Both treatments caused a general downregulation of not only signal transduction including cancer pathway proteins, but also apoptosis and chemokine pathways, with statins impacting 35 genes by twofold or greater in MDA-MB-231 and > 300 genes in Calu-1. These manifold dysregulations could also explain the various side effects reportedly caused by statins. MbetaCD produced far fewer statistical events than pravastatin in the breast cancer line but many more in the lung cell line. Pravastatin increased expression of CAV1 but caveolae density decreased and overall raft density was unaffected. MbetaCD also caused an increase in CAV1 expression and reduced the prevalence of both rafts and caveolae. It is proposed that sequestration of cholesterol from the membrane by MbetaCD is not equivalent to blockade of the cholesterol pathway and causes different effects on microdomain-mediated signal transduction dependant on the cell line. The profound effects of statins on mRNA expression can be explained by the failure of caveolin-1 to properly complex with cholesterol in an altered sterol environment, with caveolae acting as the main loci for signaling directed towards those transcription processes unaffected by MbetaCD. Targeted inhibition of the postmevalonate pathway could offer an opportunity to specifically reduce caveolae-based signaling in cancer cells. The observed impact of pravastatin on gene expression may explain the pleiotropic effects of statins when they are used as adjuvants in chemotherapy and suggests impact on gene expression as a possible cause of side effects from statin use.

Cartoon-texture regularization is a technique for reconstructing fine-scale details from ill-posed imaging problems, which are often ill-posed because of some non-invertible convolution kernel. Here we propose a cartoon-texture regularization for deblurring problems with semi-known kernel. The cartoon component is modeled by a function of bounded variation, while the texture component is measured by an approximate duality with Lipschitz functions ($W^{1,\infty}$). To approximate the dual Lipschitz norm, which is difficult to calculate, we propose an approach using concentration of measure. This provides an accurate and differentiable expression. We also present numerical results for our cartoon-texture decomposition, both in the case of a semi-known deblurring kernel and the case of a known kernel. The texture norm enables one to numerically reconstruct fine scale details that are typically difficult to recover from blurred images, and for semi-known deblurring the method quickly leads to the correct kernel, even when that kernel contains noise.

Let $\Omega\subset\mathbb R^{n+1}$, $n\geq1$, be a corkscrew domain with Ahlfors-David regular boundary. In this paper we prove that $\partial\Omega$ is uniformly $n$-rectifiable if every bounded harmonic function on $\Omega$ is $\varepsilon$-approximable or if every bounded harmonic function on $\Omega$ satisfies a suitable square-function Carleson measure estimate. In particular, this applies to the case when $\Omega=\mathbb R^{n+1}\setminus E$ and $E$ is Ahlfors-David regular. Our results solve a conjecture posed by Hofmann, Martell, and Mayboroda in a recent work where they proved the converse statements. Here we also obtain two additional criteria for uniform rectifiability. One is given in terms of the so-called "$S, Comment: Correction of a few typos and general reorganization of the arguments. Additional references

We consider solutions to the aggregation equation with Newtonian potential where the initial data are the characteristic function of a domain with boundary of class $C^{1+\gamma}$ ,$0

Introduction 67 The Study of War 68 Human Nature Explanations of War 72 Wars ‘Within’ and ‘Beyond’ States 78 Conclusion 81 Scholarship dealing with the causes of war is voluminous and multidisciplinary. This chapter describes and explains theories that have been advanced by biologists, philosophers, political scientists, and sociologists about why wars occur. It groups their ideas into categories and shows how different explanations of war give rise to different requirements or conditions for peace. It is argued that it is useful to make distinctions between immediate and underlying causes of war. The chapter pays particular attention to explanations of war based on human nature and instinct, but it also considers those psychological theories that emphasize misperception and frustration as causes of aggression. The ideas of those who find the causes of war in human collectives—states, tribes, and ethnic groups—and those who favour ‘systemic’ rather than ‘unit’ explanations are also described. The chapter also looks at the debate between ‘greed’ and ‘grievance’ as a cause of civil wars....

For d > 2, we construct a doubling measure v on ℝ d and a rectifiable curve Γ such that ν(Γ) > 0.

We prove that certain Cantor sets with non-sigma-finite onedimensional Hausdorff measure have zero analytic capacity.

because of the Carleson theorem that (2) holds if and only if every interpolation problem f(zv) = wJn i/ = 1,2,... , for {wv} G f°°, has a solution / G H°°. Although the interpolating Blaschke products comprise a small subset of the set of all Blaschke products, they play a central role in the theory ofH°°. See the last three chapters of [3]. The theorem in this paper helps explain why interpolating Blaschke products are so important in that theory.

This paper studies the transport of a mass $\mu$ in $\real^d, d \geq 2,$ by a flow field $v= -\nabla K*\mu$. We focus on kernels $K=|x|^\alpha/ \alpha$ for $2-d\leq \alpha2$ where radially symmetric solutions are known to lose monotonicity. In the case of the Newtonian potential ($\alpha=2-d$), under the assumption of radial symmetry the equation can be transformed into the inviscid Burgers equation on a half line. This enables us to prove preservation of monotonicity using the classical theory of conservation laws. In the case $2 -d < \alpha < 2$ and at the critical exponent $p$ we exhibit initial data in $L^p$ for which the solution immediately develops a Dirac mass singularity. This extends recent work on the local ill-posedness of solutions at the critical exponent., Comment: 30 pages

We propose a new variational model for image restoration using BV and Sobolev spaces. It is well known that homogeneous Sobolev spaces of negative differentiability can capture oscillatory information very well, however, just one Sobolev space hardly recognizes any difference between texture and noise. By a means of learning a series of Sobolev norms of pure texture and pure noise that will provide us with one dimensional profiles describing different behaviors of texture and noise, we will be able to make a distinction between texture and noise, and use these measurements in restoring a better image. We want to point out that our model is specifically designed to deal with noisy blurred images. Parameter insen-sitivity is one of the advantages of using a series of Sobolev spaces.

of D, then d(Tp,Tq) = d(p,q) for all TeJi\ thus maps in Ji are hyperbolic isometrics. The Schwarz-Pick theorem asserts that if/:Z)->Z) is analytic then / decreases distances, . fl .t . „ d{Ap\M)^d{p,q), (1.1) or lnnnitesimally, i-W/OI 0. Following C. McMullen, we write M(c) for the set of analytic / : / ) -> / ) such that whenever B is a hyperbolic ball in D, diam (/(£)) ^ diam(5)-c, where diam denotes diameter in the hyperbolic metric. For example, n M(C) = jt, c>0 while f(z) = z eM(c) provided c is large. This paper gives three characterizations of the set M(c). The first characterization concerns nearly isometric behavior along certain geodesies, and the second is in terms of angular derivatives at boundary points. Each/eM(c) is a Blaschke product, and the third characterization is by the distribution of the zeros. We thank Curt McMullen for bringing M(c) to our attention and for the results of the next section.