Abstract:
Aim: To determine the therapeutic effect of thy- mosin β4 (Tβ4) for treatment of ischemic limb disease in a mouse model. Methods: A mouse model of hindlimb ischemia was created by permanent ligation of femoral arteries and internal iliac artery. Tβ4 was dissolved in sterile saline and intramuscularly injected into the centre and periphery of ligation area in the treatment group (n = 10) starting from the surgery day until 4 weeks after surgery, while control animals received saline injection only (n = 9). All animals were sacrificed at 6 weeks after surgery and used for immunohistochemistry studies. Results: Tβ4 stimulated angiogenesis was evidenced by increased vascular density based on CD31 immunostaining, which was sig- nifycantly increased in Tβ4 group (562.5 ± 78.4/mm2) as compared with control group (371.1 ± 125.7/mm2; p < 0.05). The arteriole density based on CD31 and SMA dual immunostaining was similar between the Tβ4 (27.2 ± 16.9/mm2) and control (35.3 ± 6/mm2; p > 0.05) groups. Tβ4 increased Pax3/7+ skeletal muscle progenitor cell density. Pax3/7+ cell density of Tβ4 group (13.7% ± 2%) was significantly higher than that of the control group (4.3% ± 1.6%, p < 0.05). However, the numbers of central nuclei fiber and central nuclei per fiber were insignificantly increased in Tβ4 group as compared to control group. The numbers of central nuclei fiber were 8.9 ± 2.1 and 9.5 ± 1.6, and the central nuclei per fiber were 0.25 ± 0.07 and 0.48 ± 0.09 for control and Tβ4 groups, respectively. Conclusions: This preliminary study suggests that localized delivery of Tβ4 increased angiogenesis and skeletal muscle progenitor cell density in ischemic skeletal muscle, but failed to promote skeletal muscle regeneration.

Abstract:
We consider the problem of optimizing a nonlinear objective function over a weighted independence system presented by a linear-optimization oracle. We provide a polynomial-time algorithm that determines an r-best solution for nonlinear functions of the total weight of an independent set, where r is a constant that depends on certain Frobenius numbers of the individual weights and is independent of the size of the ground set. In contrast, we show that finding an optimal (0-best) solution requires exponential time even in a very special case of the problem.

Abstract:
We consider optimization of nonlinear objective functions that balance $d$ linear criteria over $n$-element independence systems presented by linear-optimization oracles. For $d=1$, we have previously shown that an $r$-best approximate solution can be found in polynomial time. Here, using an extended Erd\H{o}s-Ko-Rado theorem of Frankl, we show that for $d=2$, finding a $\rho n$-best solution requires exponential time.

Abstract:
Systems of polynomial equations over the complex or real numbers can be used to model combinatorial problems. In this way, a combinatorial problem is feasible (e.g. a graph is 3-colorable, hamiltonian, etc.) if and only if a related system of polynomial equations has a solution. In the first part of this paper, we construct new polynomial encodings for the problems of finding in a graph its longest cycle, the largest planar subgraph, the edge-chromatic number, or the largest k-colorable subgraph. For an infeasible polynomial system, the (complex) Hilbert Nullstellensatz gives a certificate that the associated combinatorial problem is infeasible. Thus, unless P = NP, there must exist an infinite sequence of infeasible instances of each hard combinatorial problem for which the minimum degree of a Hilbert Nullstellensatz certificate of the associated polynomial system grows. We show that the minimum-degree of a Nullstellensatz certificate for the non-existence of a stable set of size greater than the stability number of the graph is the stability number of the graph. Moreover, such a certificate contains at least one term per stable set of G. In contrast, for non-3- colorability, we found only graphs with Nullstellensatz certificates of degree four.

Abstract:
We consider the nonlinear integer programming problem of minimizing a quadratic function over the integer points in variable dimension satisfying a system of linear inequalities. We show that when the Graver basis of the matrix defining the system is given, and the quadratic function lies in a suitable {\em dual Graver cone}, the problem can be solved in polynomial time. We discuss the relation between this cone and the cone of positive semidefinite matrices, and show that none contains the other. So we can minimize in polynomial time some non-convex and some (including all separable) convex quadrics. We conclude by extending our results to efficient integer minimization of multivariate polynomial functions of arbitrary degree lying in suitable cones.

Abstract:
We address optimization of nonlinear functions of the form $f(Wx)$, where $f:\R^d\to \R$ is a nonlinear function, $W$ is a $d\times n$ matrix, and feasible $x$ are in some large finite set $F$ of integer points in $\R^n$. One motivation is multi-objective discrete optimization, where $f$ trades off the linear functions given by the rows of $W$. Another motivation is to extend known results about polynomial-time linear optimization over discrete structures to nonlinear optimization. We assume that the convex hull of $F$ is well-described by linear inequalities. For example, the set of characteristic vectors of common bases of a pair of matroids on a common ground set. When $F$ is well described, $f$ is convex (or even quasiconvex), and $W$ has a fixed number of rows and is unary encoded or with entries in a fixed set, we give an efficient deterministic algorithm for maximization. When $F$ is well described, $f$ is a norm, and binary-encoded $W$ is nonnegative, we give an efficient deterministic constant-approximation algorithm for maximization. When $F$ is well described, $f$ is ``ray concave'' and non-decreasing, and $W$ has a fixed number of rows and is unary encoded or with entries in a fixed set, we give an efficient deterministic constant-approximation algorithm for minimization. When $F$ is the set of characteristic vectors of common bases of a pair of vectorial matroids on a common ground set, $f$ is arbitrary, and $W$ has a fixed number of rows and is unary encoded, we give an efficient randomized algorithm for optimization.

Abstract:
Large photon-number path entanglement is an important resource for enhanced precision measurements and quantum imaging. We present a general constructive protocol to create any large photon number path-entangled state based on the conditional detection of single photons. The influence of imperfect detectors is considered and an asymptotic scaling law is derived.

Abstract:
The manipulation of quantum entanglement has found enormous potential for improving performances of devices such as gyroscopes, clocks, and even computers. Similar improvements have been demonstrated for lithography and microscopy. We present an overview of some aspects of enhancement by quantum entanglement in imaging and metrology.

Abstract:
Heisenberg-limited measurement protocols can be used to gain an increase in measurement precision over classical protocols. Such measurements can be implemented using, e.g., optical Mach-Zehnder interferometers and Ramsey spectroscopes. We address the formal equivalence between the Mach-Zehnder interferometer, the Ramsey spectroscope, and the discrete Fourier transform. Based on this equivalence we introduce the ``quantum Rosetta stone'', and we describe a projective-measurement scheme for generating the desired correlations between the interferometric input states in order to achieve Heisenberg-limited sensitivity. The Rosetta stone then tells us the same method should work in atom spectroscopy.

Abstract:
Optical quantum nondemolition devices can provide essential tools for quantum information processing. Here, we describe several optical interferometers that signal the presence of a single photon in a particular input state without destroying it. We discuss both entanglement-assisted and non-entanglement-assisted interferometers, with ideal and realistic detectors. We found that existing detectors with 88% quantum efficiency and single-photon resolution can yield output fidelities of up to 89%, depending on the input state. Furthermore, we construct expanded protocols to perform QND detections of single photons that leave the polarization invariant. For detectors with 88% efficiency we found polarization-preserving output fidelities of up to 98.5%.