Private Incremental Regression

Data is continuously generated by modern data sources, and a recent challenge in machine learning has been to develop techniques that perform well in an incremental (streaming) setting. In this paper, we investigate the problem of private machine learning, where as common in practice, the data is not given at once, but rather arrives incrementally over time. We introduce the problems of private incremental ERM and private incremental regression where the general goal is to always maintain a good empirical risk minimizer for the history observed under differential privacy. Our first contribution is a generic transformation of private batch ERM mechanisms into private incremental ERM mechanisms, based on a simple idea of invoking the private batch ERM procedure at some regular time intervals. We take this construction as a baseline for comparison. We then provide two mechanisms for the private incremental regression problem. Our first mechanism is based on privately constructing a noisy incremental gradient function, which is then used in a modified projected gradient procedure at every timestep. This mechanism has an excess empirical risk of $\approx\sqrt{d}$, where $d$ is the dimensionality of the data. While from the results of [Bassily et al. 2014] this bound is tight in the worst-case, we show that certain geometric properties of the input and constraint set can be used to derive significantly better results for certain interesting regression problems.Comment: To appear in PODS 201

The Traveling Salesman Problem: Low-Dimensionality Implies a Polynomial Time Approximation Scheme

The Traveling Salesman Problem (TSP) is among the most famous NP-hard optimization problems. We design for this problem a randomized polynomial-time algorithm that computes a (1+eps)-approximation to the optimal tour, for any fixed eps>0, in TSP instances that form an arbitrary metric space with bounded intrinsic dimension. The celebrated results of Arora (A-98) and Mitchell (M-99) prove that the above result holds in the special case of TSP in a fixed-dimensional Euclidean space. Thus, our algorithm demonstrates that the algorithmic tractability of metric TSP depends on the dimensionality of the space and not on its specific geometry. This result resolves a problem that has been open since the quasi-polynomial time algorithm of Talwar (T-04)

Probing astrophysically important states in the ²⁶Mg nucleus to study neutron sources for the s process

Background: The ²²Ne(α,n) ²⁵Mg reaction is the dominant neutron source for the slow neutron capture process (s process) in massive stars, and contributes, together with C¹³(α,n)O¹⁶, to the production of neutrons for the s process in asymptotic giant branch (AGB) stars. However, the reaction is endothermic and competes directly with ²²Ne(α,γ)²⁶Mg radiative capture. The uncertainties for both reactions are large owing to the uncertainty in the level structure of ²⁶Mg near the α and neutron separation energies. These uncertainties affect the s-process nucleosynthesis calculations in theoretical stellar models. Purpose: Indirect studies in the past have been successful in determining the energies and the γ-ray and neutron widths of the Mg26 states in the energy region of interest. But, the high Coulomb barrier hinders a direct measurement of the resonance strengths, which are determined by the α widths for these states. The goal of the present experiments is to identify the critical resonance states and to precisely measure the α widths by α-transfer techniques. Methods: The α-inelastic scattering and α-transfer measurements were performed on a solid ²⁶Mg target and a ²²Ne gas target, respectively, using the Grand Raiden Spectrometer at the Research Center for Nuclear Physics in Osaka, Japan. The (α,α′) measurements were performed at 0.45°, 4.1°, 8.6°, and 11.1° and the (⁶Li,d) measurements at 0° and 10°. The scattered α particles and deuterons were detected by the focal plane detection system consisting of multiwire drift chambers and plastic scintillators. The focal plane energy calibration allowed the study of ²⁶Mg levels from Eₓ = 7.69–12.06 MeV in the (α,α′) measurement and Eₓ = 7.36–11.32 MeV in the (⁶Li,d) measurement. Results: Six levels (Eₓ = 10717, 10822, 10951, 11085, 11167, and 11317 keV) were observed above the α threshold in the region of interest (10.61–11.32 MeV). The α widths were calculated for these states from the experimental data. The results were used to determine the α-capture induced reaction rates. Conclusion: The energy range above the α threshold in ²⁶Mg was investigated using a high resolution spectrometer. A number of states were observed for the first time in α-scattering and α-transfer reactions. The excitation energies and spin-parities were determined. Good agreement is observed for previously known levels in ²⁶Mg. From the observed resonance levels the Eₓ = 10717 keV state has a negligible contribution to the α-induced reaction rates. The rates are dominated in both reaction channels by the resonance contributions of the states at Ex = 10951, 11167, and 11317 keV. The Eₓ = 11167 keV state has the most appreciable impact on the (α,γ) rate and therefore plays an important role in the prediction of the neutron production in s-process environments

Stellar 36,38^{36,38}Ar(n,γ)37,39(n,\gamma)^{37,39}Ar reactions and their effect on light neutron-rich nuclide synthesis

The $^{36}$Ar$(n,\gamma)^{37}$Ar ($t_{1/2}$ = 35 d) and $^{38}$Ar$(n,\gamma)^{39}$Ar (269 y) reactions were studied for the first time with a quasi-Maxwellian ($kT \sim 47$ keV) neutron flux for Maxwellian Average Cross Section (MACS) measurements at stellar energies. Gas samples were irradiated at the high-intensity Soreq applied research accelerator facility-liquid-lithium target neutron source and the $^{37}$Ar/$^{36}$Ar and $^{39}$Ar/$^{38}$Ar ratios in the activated samples were determined by accelerator mass spectrometry at the ATLAS facility (Argonne National Laboratory). The $^{37}$Ar activity was also measured by low-level counting at the University of Bern. Experimental MACS of $^{36}$Ar and $^{38}$Ar, corrected to the standard 30 keV thermal energy, are 1.9(3) mb and 1.3(2) mb, respectively, differing from the theoretical and evaluated values published to date by up to an order of magnitude. The neutron capture cross sections of $^{36,38}$Ar are relevant to the stellar nucleosynthesis of light neutron-rich nuclides; the two experimental values are shown to affect the calculated mass fraction of nuclides in the region A=36-48 during the weak $s$-process. The new production cross sections have implications also for the use of $^{37}$Ar and $^{39}$Ar as environmental tracers in the atmosphere and hydrosphere.Comment: 18 pages + Supp. Mat. (13 pages) Accepted for publication in Phys. Rev. Let

The first direct measurement of ¹²C (¹²C,n) ²³Mg at stellar energies

Neutrons produced by the carbon fusion reaction ¹²C(¹²C,n)²³Mg play an important role in stellar nucleosynthesis. However, past studies have shown large discrepancies between experimental data and theory, leading to an uncertain cross section extrapolation at astrophysical energies. We present the first direct measurement that extends deep into the astrophysical energy range along with a new and improved extrapolation technique based on experimental data from the mirror reaction ¹²C(¹²C,p)²³Na. The new reaction rate has been determined with a well-defined uncertainty that exceeds the precision required by astrophysics models. Using our constrained rate, we find that ¹²C(¹²C,n)²³Mg is crucial to the production of Na and Al in Pop-III Pair Instability Supernovae. It also plays a non-negligible role in the production of weak s-process elements as well as in the production of the important galacti

Ultrafast optical generation of coherent phonons in CdTe1-xSex quantum dots

We report on the impulsive generation of coherent optical phonons in CdTe0.68Se0.32 nanocrystallites embedded in a glass matrix. Pump probe experiments using femtosecond laser pulses were performed by tuning the laser central energy to resonate with the absorption edge of the nanocrystals. We identify two longitudinal optical phonons, one longitudinal acoustic phonon and a fourth mode of a mixed longitudinal-transverse nature. The amplitude of the optical phonons as a function of the laser central energy exhibits a resonance that is well described by a model based on impulsive stimulated Raman scattering. The phases of the coherent phonons reveal coupling between different modes. At low power density excitations, the frequency of the optical coherent phonons deviates from values obtained from spontaneous Raman scattering. This behavior is ascribed to the presence of electronic impurity states which modify the nanocrystal dielectric function and, thereby, the frequency of the infrared-active phonons

Low serum magnesium and 1-year mortality in alcohol withdrawal syndrome

Background: In 2014, the WHO reported that 6% of all deaths were attributable to excess alcohol consumption. The aim of the present study was to examine the relationship between serum magnesium concentrations and mortality in patients with alcohol withdrawal syndrome (AWS). Materials and methods: A retrospective review of 700 patients with documented evidence of previous AWS indicating a requirement for benzodiazepine prophylaxis or evidence of alcohol withdrawal syndrome between November 2014 and March 2015. Results: Of 380 patients included in the sample analysis, 64 (17%) were dead at 1 year following the time of treatment for AWS. The majority of patients had been prescribed thiamine (77%) and a proton pump inhibitor (66%). In contrast, the majority of patients had low circulating magnesium concentrations (2 (P  50 years (OR 3.37, 95% CI 1.52-7.48, P 2 (OR 3.10, 95% CI 1.38-6.94, P < 0.01) and magnesium < 0.75 mmol/L (OR 4.11, 95% CI 1.3-12.8, P < 0.05) remained independently associated with death at 1 year. Conclusion: Overall, 1-year mortality was significantly higher among those patients who were magnesium deficient (<0.75 mmol/L) when compared to those who were replete (≥0.75 mmol/L; P < 0.001)

Message Passing for Optimization and Control of Power Grid: Model of Distribution System with Redundancy

We use a power grid model with $M$ generators and $N$ consumption units to optimize the grid and its control. Each consumer demand is drawn from a predefined finite-size-support distribution, thus simulating the instantaneous load fluctuations. Each generator has a maximum power capability. A generator is not overloaded if the sum of the loads of consumers connected to a generator does not exceed its maximum production. In the standard grid each consumer is connected only to its designated generator, while we consider a more general organization of the grid allowing each consumer to select one generator depending on the load from a pre-defined consumer-dependent and sufficiently small set of generators which can all serve the load. The model grid is interconnected in a graph with loops, drawn from an ensemble of random bipartite graphs, while each allowed configuration of loaded links represent a set of graph covering trees. Losses, the reactive character of the grid and the transmission-level connections between generators (and many other details relevant to realistic power grid) are ignored in this proof-of-principles study. We focus on the asymptotic limit and we show that the interconnects allow significant expansion of the parameter domains for which the probability of a generator overload is asymptotically zero. Our construction explores the formal relation between the problem of grid optimization and the modern theory of sparse graphical models. We also design heuristic algorithms that achieve the asymptotically optimal selection of loaded links. We conclude discussing the ability of this approach to include other effects, such as a more realistic modeling of the power grid and related optimization and control algorithms.Comment: 10 page

Anti-tumor effect of Liqi, a traditional Chinese medicine prescription, in tumor bearing mice

<p>Abstract</p> <p>Background</p> <p><it>Liqi</it>, an herbal preparation used in traditional Chinese medicine, has been used to treat cancer in China for centuries. We investigated the anti-tumor effects of liqi and their mechanisms in mice that had been xenografted with tumors.</p> <p>Methods</p> <p>Sarcoma 180 tumor, Lewis lung carcinoma, and SGC-7901 cells were implanted in BALB/c mice, C57BL/6 mice, and BALB/c nude mice, respectively. Liqi was administered to subgroups of these mice. The tumor weight and size were measured. Cell cycle analysis and T lymphocyte subsets were determined by flow cytometry. The activity of NK cells and TNF was tested using cytotoxicity assay on YAC-1 cells and L929 cells, respectively, and the activity of IL-2 was tested with an IL-2-dependent CTLL-2 cell proliferation assay. Platelet aggregation was monitored by measuring electric impedance, and the levels of thromboxane A2 (TXA₂) and prostacyclin (PGI₂) in blood were measured by ¹²⁵I-TXB₂and ¹²⁵I-Keto-PGF_1αradioimmunoassay.</p> <p>Results</p> <p>The results showed that liqi inhibited tumor growth in tumor-implanted mice and arrested the cell proliferation in the G0/G1 phase and reduced the portion of cells in S and G2/M phase for SGC-7901 cells. Liqi increased the activity of NK cells and TNF-α, stimulated IL-2 production and activity, and regulated T lymphocyte subpopulations. Liqi inhibited the Lewis lung carcinoma metastasis by inhibiting platelet aggregation and normalizing the balance between TXA₂and PGI₂.</p> <p>Conclusion</p> <p>All these findings demonstrated that liqi has an anti-tumor effect in vivo. The mechanism may be related to immune regulation and anticoagulation effects.</p