Transient Repetitive Exposure to Low Level Light Therapy Enhances Collateral Blood Vessel Growth in The Ischemic Hindlimb of The Tight Skin Mouse

The tight skin mouse (Tsk^?/+) is a model of scleroderma characterized by impaired vasoreactivity, increased oxidative stress, attenuated angiogenic response to VEGF and production of the angiogenesis inhibitor angiostatin. Low‐level light therapy (LLLT) stimulates angiogenesis in myocardial infarction and chemotherapy‐induced mucositis. We hypothesize that repetitive LLLT restores vessel growth in the ischemic hindlimb of Tsk^?/+ mice by attenuating angiostatin and enhancing angiomotin effects in vivo. C57Bl/6J and Tsk^?/+ mice underwent ligation of the femoral artery. Relative blood flow to the foot was measured using a laser Doppler imager. Tsk^?/+ mice received LLLT (670 nm, 50 mW cm^?2, 30 J cm^?2) for 10 min per day for 14 days. Vascular density was determined using lycopersicom lectin staining. Immunofluorescent labeling, Western blot analysis and immunoprecipitation were used to determine angiostatin and angiomotin expression. Recovery of blood flow to the ischemic limb was reduced in Tsk^?/+ compared with C57Bl/6 mice 2 weeks after surgery. LLLT treatment of Tsk^?/+ mice restored blood flow to levels observed in C57Bl/6 mice. Vascular density was decreased, angiostatin expression was enhanced and angiomotin depressed in the ischemic hindlimb of Tsk^?/+ mice. LLLT treatment reversed these abnormalities. LLLT stimulates angiogenesis by increasing angiomotin and decreasing angiostatin expression in the ischemic hindlimb of Tsk^?/+ mice.     

Approaches to Effective Semi-Continuity of Real Functions

For semi-continuous real functions we study different computability concepts defined via computability of epigraphs and hypographs. We call a real function f lower semi-computable of type one, if its open hypograph hypo(f) is recursively enumerably open in dom(f) × ?; we call f lower semi-computable of type two, if its closed epigraph Epi(f) is recursively enumerably closed in dom(f) × ?; we call f lower semi-computable of type three, if Epi(f) is recursively closed in dom(f) × ?. We show that type one and type two semi-computability are independent and that type three semi-computability plus effectively uniform continuity implies computability, which is false for type one and type two instead of type three. We show also that the integral of a type three semi-computable real function on a computable interval is not necessarily computable.     

A Characterization of Effective Resistance Metrics

Potential Analysis - We produce a characterization of finite metric spaces which are given by the effective resistance of a graph. This characterization is applied to the more general context of...     

Is wave propagation computable or can wave computers beat the turing machine?

According to the Church-Turing Thesis a number function is computableby the mathematically defined Turing machine if and only ifit is computable by a physical machine. In 1983 Pour-El andRichards defined a three-dimensional wave u(t,x) such that theamplitude u(0,x) at time 0 is computable and the amplitude u(1,x)at time 1 is continuous but not computable. Therefore, theremight be some kind of wave computer beating the Turing machine.By applying the framework of Type 2 Theory of Effectivity (TTE),in this paper we analyze computability of wave propagation.In particular, we prove that the wave propagator is computableon continuously differentiable waves, where one derivative islost, and on waves from Sobolev spaces. Finally, we explainwhy the Pour-El-Richards result probably does not help to designa wave computer which beats the Turing machine. 2000 Mathematical Subject Classification: 03D80, 03F60, 35L05,68Q05.     

Weakly Computable Real Numbers

A real number x is recursively approximable if it is a limit of a computable sequence of rational numbers. If, moreover, the sequence is increasing (decreasing or simply monotonic), then x is called left computable (right computable or semi-computable). x is called weakly computable if it is a difference of two left computable real numbers. We show that a real number is weakly computable if and only if there is a computable sequence (x_s)_s of rational numbers which converges to x weakly effectively, namely the sum of jumps of the sequence is bounded. It is also shown that the class of weakly computable real numbers extends properly the class of semi-computable real numbers and the class of recursively approximable real numbers extends properly the class of weakly computable real numbers.     

The Arithmetical Hierarchy of Real Numbers

A real number x is computable iff it is the limit of an effectively converging computable sequence of rational numbers, and x is left (right) computable iff it is the supremum (infimum) of a computable sequence of rational numbers. By applying the operations “sup” and “inf” alternately n times to computable (multiple) sequences of rational numbers we introduce a non‐collapsing hierarchy {Σ_n, Π_n, Δ_n : n ∈ ℕ} of real numbers. We characterize the classes Σ₂, Π₂ and Δ₂ in various ways and give several interesting examples.     

Computing Schrödinger propagators on Type-2 Turing machines

We study Turing computability of the solution operators of the initial-value problems for the linear Schrödinger equation u_t=iΔu+φ and the nonlinear Schrödinger equation of the form iu_t=-Δu+mu+|u|²u. We prove that the solution operators are computable if the initial data are Sobolev functions but noncomputable in the linear case if the initial data are L^p-functions and p≠2. The computations are performed on Type-2 Turing machines.     

Robustness and applicability of Markov chain Monte Carlo algorithms for eigenvalue problems

In this paper we analyse applicability and robustness of Markov chain Monte Carlo algorithms for eigenvalue problems. We restrict our consideration to real symmetric matrices.

Almost Optimal Monte Carlo (MAO) algorithms for solving eigenvalue problems are formulated. Results for the structure of both – systematic and probability error are presented. It is shown that the values of both errors can be controlled independently by different algorithmic parameters. The results present how the systematic error depends on the matrix spectrum. The analysis of the probability error is presented. It shows that the close (in some sense) the matrix under consideration is to the stochastic matrix the smaller is this error. Sufficient conditions for constructing robust and interpolation Monte Carlo algorithms are obtained. For stochastic matrices an interpolation Monte Carlo algorithm is constructed.

A number of numerical tests for large symmetric dense matrices are performed in order to study experimentally the dependence of the systematic error from the structure of matrix spectrum. We also study how the probability error depends on the balancing of the matrix.     

On the complexity of online computations of real functions

A reasonable computational complexity theory for real functions is obtained by using the modified infinite binary representation with digits 0, l, and −1 for the real numbers and Turing machines which transform with one-way output modified binary input sequences into modified binary output sequences. As the main result of this paper it is shown that there is a trade-off between the input lookahead, i.e., the deviation of online computation and the computational complexity for machines computing certain real functions.     

Methods for the isolation and characterization of constituents of natural products: XVIII. A micro-bisulfite column for extracting aldehydes and certain ketones

A procedure using a sodium bisulfite-Celite column was modified for extraction of micromole amounts of aldehydes and certain ketones from nonaqueous solution. Quantitative removal of saturated and unsaturatcd normal chain aliphatic and aromatic aldehydes takes place rapidly, but under the same conditions aldehydes branched on the alpha carbon atom fail to extract quantitatively or at all. Acetone, cyclopentanone and cyclohexanone were removed quantitatively hut higher members in both classes were not. Vicinal diketones were extracted quantitatively. A scaled-down version conducted in a melting point capillary and suitable for microliter volumes containing microgram amounts of carbonyls also was tested.