A polynomial-time algorithm for optimizing over N-fold 4-block decomposable integer programs

In this paper we generalize N-fold integer programs and two-stage integer programs with N scenarios to N-fold 4-block decomposable integer programs. We show that for fixed blocks but variable N, these integer programs are polynomial-time solvable for any linear objective. Moreover, we present a polynomial-time computable optimality certificate for the case of fixed blocks, variable N and any convex separable objective function. We conclude with two sample applications, stochastic integer programs with second-order dominance constraints and stochastic integer multi-commodity flows, which (for fixed blocks) can be solved in polynomial time in the number of scenarios and commodities and in the binary encoding length of the input data. In the proof of our main theorem we combine several non-trivial constructions from the theory of Graver bases. We are confident that our approach paves the way for further extensions

A polynomial oracle-time algorithm for convex integer minimization

In this paper we consider the solution of certain convex integer minimization problems via greedy augmentation procedures. We show that a greedy augmentation procedure that employs only directions from certain Graver bases needs only polynomially many augmentation steps to solve the given problem. We extend these results to convex $N$-fold integer minimization problems and to convex 2-stage stochastic integer minimization problems. Finally, we present some applications of convex $N$-fold integer minimization problems for which our approach provides polynomial time solution algorithms.Comment: 19 pages, 1 figur

Low temperature spin fluctuations in geometrically frustrated Yb3Ga5O12

In the garnet structure compound Yb3Ga5O12, the Yb3+ ions (ground state effective spin S' = 1/2) are situated on two interpenetrating corner sharing triangular sublattices such that frustrated magnetic interactions are possible. Previous specific heat measurements evidenced the development of short range magnetic correlations below 0.5K and a lambda-transition at 54mK (Filippi et al. J. Phys. C: Solid State Physics 13 (1980) 1277). From 170-Yb M"ossbauer spectroscopy measurements down to 36mK, we find there is no static magnetic order at temperatures below that of the lambda-transition. Below 0.3K, the fluctuation frequency of the short range correlated Yb3+ moments progressively slows down and as the temperature tends to 0, the frequency tends to a quasi-saturated value of 3 x 10^9 s^-1. We also examined the Yb3+ paramagnetic relaxation rates up to 300K using 172-Yb perturbed angular correlation measurements: they evidence phonon driven processes.Comment: 6 pages, 5 figure

Learning intrinsic excitability in medium spiny neurons

We present an unsupervised, local activation-dependent learning rule for intrinsic plasticity (IP) which affects the composition of ion channel conductances for single neurons in a use-dependent way. We use a single-compartment conductance-based model for medium spiny striatal neurons in order to show the effects of parametrization of individual ion channels on the neuronal activation function. We show that parameter changes within the physiological ranges are sufficient to create an ensemble of neurons with significantly different activation functions. We emphasize that the effects of intrinsic neuronal variability on spiking behavior require a distributed mode of synaptic input and can be eliminated by strongly correlated input. We show how variability and adaptivity in ion channel conductances can be utilized to store patterns without an additional contribution by synaptic plasticity (SP). The adaptation of the spike response may result in either "positive" or "negative" pattern learning. However, read-out of stored information depends on a distributed pattern of synaptic activity to let intrinsic variability determine spike response. We briefly discuss the implications of this conditional memory on learning and addiction.Comment: 20 pages, 8 figure

Raised FGF23 Correlates to Increased Mortality in Critical Illness, Independent of Vitamin D

BACKGROUND: Fibroblast Growth Factor (FGF23) is an endocrine hormone classically associated with the homeostasis of vitamin D, phosphate, and calcium. Elevated serum FGF23 is a known independent risk factor for mortality in chronic kidney disease (CKD) patients. We aimed to determine if there was a similar relationship between FGF23 levels and mortality in critically ill patients.METHODS: Plasma FGF23 levels were measured by ELISA in two separate cohorts of patients receiving vitamin D supplementation: critical illness patients (VITdAL-ICU trial, n = 475) and elective oesophagectomy patients (VINDALOO trial, n = 76). Mortality data were recorded at 30 and 180 days or at two years, respectively. FGF23 levels in a healthy control cohort were also measured ( n = 27). RESULTS: Elevated FGF23 (quartile 4 vs. quartiles 1-3) was associated with increased short-term (30 and 180 day) mortality in critical illness patients ( p &lt; 0.001) and long-term (two-year) mortality in oesophagectomy patients ( p = 0.0149). Patients who died had significantly higher FGF23 levels than those who survived: In the critical illness cohort, those who died had 1194.6 pg/mL (range 0-14,000), while those who survived had 120.4 pg/mL (range = 15-14,000) ( p = 0.0462). In the oesophagectomy cohort, those who died had 1304 pg/mL (range = 154-77,800), while those who survived had 644 pg/mL (range = 179-54,894) ( p &lt; 0.001). This was found to be independent of vitamin D or CKD status (critical illness p = 0.3507; oesophagectomy p = 0.3800). FGF23 levels in healthy controls were similar to those seen in oesophagectomy patients ( p = 0.4802). CONCLUSIONS: Elevated baseline serum FGF23 is correlated with increased mortality in both the post-oesophagectomy cohort and the cohort of patients with critical illness requiring intensive care admission. This was independent of vitamin D status, supplementation, or CKD status, which suggests the presence of vitamin D-independent mechanisms of FGF23 action during the acute and convalescent stages of critical illness, warranting further investigation.</p

Thermodynamic Study of Excitations in a 3D Spin Liquid

In order to characterize thermal excitations in a frustrated spin liquid, we have examined the magnetothermodynamics of a model geometrically frustrated magnet. Our data demonstrate a crossover in the nature of the spin excitations between the spin liquid phase and the high-temperature paramagnetic state. The temperature dependence of both the specific heat and magnetization in the spin liquid phase can be fit within a simple model which assumes that the spin excitations have a gapped quadratic dispersion relation.Comment: 5 figure

On the well-posedness of uncalibrated photometric stereo under general lighting

Uncalibrated photometric stereo aims at estimating the 3D-shape of a surface, given a set of images captured from the same viewing angle, but under unknown, varying illumination. While the theoretical foundations of this inverse problem under directional lighting are well-established, there is a lack of mathematical evidence for the uniqueness of a solution under general lighting. On the other hand, stable and accurate heuristical solutions of uncalibrated photometric stereo under such general lighting have recently been proposed. The quality of the results demonstrated therein tends to indicate that the problem may actually be well-posed, but this still has to be established. The present paper addresses this theoretical issue, considering first-order spherical harmonics approximation of general lighting. Two important theoretical results are established. First, the orthographic integrability constraint ensures uniqueness of a solution up to a global concave-convex ambiguity , which had already been conjectured, yet not proven. Second, the perspective integrability constraint makes the problem well-posed, which generalizes a previous result limited to directional lighting. Eventually, a closed-form expression for the unique least-squares solution of the problem under perspective projection is provided , allowing numerical simulations on synthetic data to empirically validate our findings