Semismall perturbations, semi-intrinsic ultracontractivity, and integral representations of nonnegative solutions for parabolic equations

We consider nonnegative solutions of a parabolic equation in a cylinder D \timesI, where $D$ is a noncompact domain of a Riemannian manifold and $I =(0,T)$ with $0 < T \le \infty$ or $I=(-\infty,0)$. Under the assumption [SSP] (i.e., the constant function 1 is a semismall perturbation of the associated elliptic operator on $D$), we establish an integral representation theorem of nonnegative solutions: In the case $I =(0,T)$, any nonnegative solution is represented uniquely by an integral on $(D \times \{0 \}) \cup (\partial_M D \times [0,T))$, where $\partial_M D$ is the Martin boundary of $D$ for the elliptic operator; and in the case $I=(-\infty,0)$, any nonnegative solution is represented uniquely by the sum of an integral on $\partial_M D \times (-\infty,0)$ and a constant multiple of a particular solution. We also show that [SSP] implies the condition [SIU] (i.e., the associated heat kernel is semi-intrinsically ultracontractive).Comment: 35 page

Firms' Main Market, Human Capital and Wages

Recent international trade literature emphasizes two features in characterizing the current patterns of trade: efficiency heterogeneity at the firm level and quality differentiation. This paper explores human capital and wage differences across firms in that context. We build a partial equilibrium model predicting that firms selling in more-remote markets employ higher human capital and pay higher wages to employees within each education group. The channel linking these variables is firms’ endogenous choice of quality. Predictions are tested using Spanish employer-employee matched data that classify firms according to four main destination markets: local, national, European Union, and rest of the World. Employees’ average education is increasing in the remoteness of firm’s main output market. Market–destination wage premia are large, increasing in the remoteness of the market, and increasing in individual education. These results suggest that increasing globalization may play a significant role in raising wage inequality within and across education groups.vertical differentiation, exporters, Alchian-Allen effect, wage inequality, unobservable skills

Financial liberalization and the capital account : Thailand, 1988-97

The authors examine Thailand's macro-economy and micro-economy for the period 1988-97 to assess the extent to which the country's mix of macroeconomic and financial sector policies contributed to its economic crisis in 1997. They conclude that the crisis was fundamentally one of private sector debt, rooted in private behavior that affected the magnitude and composition of investment and how it was financed. Unlike the Latin American debt crisis, the Thai crisis was not caused by excessive sovereign borrowing. Financial sector weakness--including inadequate regulation and supervision, implicit deposit insurance, concentrated ownership structures, and poor accounting and disclosure--combined with liberalization of the financial sector and capital accounts, increased vulnerability by creating incentives for risk-taking by financial institutions. Many macroeconomic fundamentals were strong, but the combination of tight monetary policy and an inflexible exchange rate created strong incentives for residents to expose themselves to excessive foreign exchange and liquidity risks. Weak corporate governance, including close corporate links to the banking sector, encouraged risky investments and over-diversification in the corporate sector.Payment Systems&Infrastructure,Financial Intermediation,Banks&Banking Reform,International Terrorism&Counterterrorism,Economic Theory&Research,Banks&Banking Reform,Financial Intermediation,Economic Theory&Research,International Terrorism&Counterterrorism,Financial Economics

On dynamical bit sequences

Let X^{(k)}(t) = (X_1(t), ..., X_k(t)) denote a k-vector of i.i.d. random variables, each taking the values 1 or 0 with respective probabilities p and 1-p. As a process indexed by non-negative t, $X^{(k)}(t)$ is constructed--following Benjamini, Haggstrom, Peres, and Steif (2003)--so that it is strong Markov with invariant measure ((1-p)\delta_0+p\delta_1)^k. We derive sharp estimates for the probability that ``X_1(t)+...+X_k(t)=k-\ell for some t in F,'' where F \subset [0,1] is nonrandom and compact. We do this in two very different settings: (i) Where \ell is a constant; and (ii) Where \ell=k/2, k is even, and p=q=1/2. We prove that the probability is described by the Kolmogorov capacitance of F for case (i) and Howroyd's 1/2-dimensional box-dimension profiles for case (ii). We also present sample-path consequences, and a connection to capacities that answers a question of Benjamini et. al. (2003)Comment: 25 pages. This a substantial revision of an earlier paper. The material has been reorganized, and Theorem 1.3 is ne

Spatial inhomogeneities in the sedimentation of biogenic particles in ocean flows: analysis in the Benguela region

Sedimentation of particles in the ocean leads to inhomogeneous horizontal distributions at depth, even if the release process is homogeneous. We study this phenomenon considering a horizontal sheet of sinking particles immersed in an oceanic flow, and determine how the particles are distributed when they sediment on the seabed (or are collected at a given depth). The study is performed from a Lagrangian viewpoint attending to the properties of the oceanic flow and the physical characteristics (size and density) of typical biogenic sinking particles. Two main processes determine the distribution, the stretching of the sheet caused by the flow and its projection on the surface where particles accumulate. These mechanisms are checked, besides an analysis of their relative importance to produce inhomogeneities, with numerical experiments in the Benguela region. Faster (heavier or larger) sinking particles distribute more homogeneously than slower ones.Comment: 24 pages, 8 figures. To appear in J. Geophys. Res.-Ocean

Tensor Analysis and Fusion of Multimodal Brain Images

Current high-throughput data acquisition technologies probe dynamical systems with different imaging modalities, generating massive data sets at different spatial and temporal resolutions posing challenging problems in multimodal data fusion. A case in point is the attempt to parse out the brain structures and networks that underpin human cognitive processes by analysis of different neuroimaging modalities (functional MRI, EEG, NIRS etc.). We emphasize that the multimodal, multi-scale nature of neuroimaging data is well reflected by a multi-way (tensor) structure where the underlying processes can be summarized by a relatively small number of components or "atoms". We introduce Markov-Penrose diagrams - an integration of Bayesian DAG and tensor network notation in order to analyze these models. These diagrams not only clarify matrix and tensor EEG and fMRI time/frequency analysis and inverse problems, but also help understand multimodal fusion via Multiway Partial Least Squares and Coupled Matrix-Tensor Factorization. We show here, for the first time, that Granger causal analysis of brain networks is a tensor regression problem, thus allowing the atomic decomposition of brain networks. Analysis of EEG and fMRI recordings shows the potential of the methods and suggests their use in other scientific domains.Comment: 23 pages, 15 figures, submitted to Proceedings of the IEE

A Note on the Link between Firm Size and Exports

This paper re-examines the link between firm size and exports in order to study the proposal that consists of increasing the firm size to raise exports as a way out of the current economic crisis. The elasticity of export propensity (percentage of exported sales) with respect to firm size depends on several firm characteristics. The new theories of international trade emphasize the firm heterogeneity as the theoretical basis of this behaviour. In the context of such heterogeneity, this paper uses the quantile regression methodology to analyze the effect of firm size on export propensity of the firms, confirming the existence of a positive relationship that becomes less important as export propensity increases. The traditional estimate of this elasticity on the average of the export propensities distribution underestimates the effect in the bottom of the distribution and overestimates the effect on most of it

Electrochemical determination of an antitumour platinum(IV) complex: trans-[PtCl2(OH)2(dimethylamine)(isopro­pylamine)]. Application to biological samples

A differential pulse voltammetry (DPV) method has been applied for the first time for determination of trans-Pt[Cl2(OH)2(dimethylamine)(isopropylamine)]. To this end, all chemical and instrumental variables affecting the determination of trans-Pt[Cl2(OH)2(dimethylamine)(isopropylamine)] were optimized. From studies of the mechanisms governing the electrochemical response of trans-Pt[Cl2(OH)2(dimethylamine)(isopropylamine)], it was concluded that it is an electrochemically irreversible system with a reduc­tion under diffusion control, with a reduction potential of -425 mV. Under optimal conditions, the variation in the analytical signal (Ip) with trans-Pt[Cl2(OH)2(dimethylamine)(isopropylamine)] concentration is linear in the 0.8 µg mL-1 to 20 µg mL-1 range, with an LOD of 97 ng mL-1 and a LOQ of 323 ng mL-1, RSD = 1.58 % and Er = 0.83 %. The optimized method was applied to the determination of trans-Pt[Cl2(OH)2(di-methylamine)(isopropylamine)] in biological fluids, human urine and synthetic urin