Private Multiplicative Weights Beyond Linear Queries

A wide variety of fundamental data analyses in machine learning, such as linear and logistic regression, require minimizing a convex function defined by the data. Since the data may contain sensitive information about individuals, and these analyses can leak that sensitive information, it is important to be able to solve convex minimization in a privacy-preserving way. A series of recent results show how to accurately solve a single convex minimization problem in a differentially private manner. However, the same data is often analyzed repeatedly, and little is known about solving multiple convex minimization problems with differential privacy. For simpler data analyses, such as linear queries, there are remarkable differentially private algorithms such as the private multiplicative weights mechanism (Hardt and Rothblum, FOCS 2010) that accurately answer exponentially many distinct queries. In this work, we extend these results to the case of convex minimization and show how to give accurate and differentially private solutions to *exponentially many* convex minimization problems on a sensitive dataset

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

Impact of Dwell Angle on the Electromagnetic Torque Ripplesof the Switched Reluctance Motor

Switched reluctance motors (SRM) are emerging as promising competitors to the vector-controlled induction motor (VCIM) drives and permanent magnet (PM) motor drives in the variable-speed drive market owing to their robust nature coupled with low cost, simplicity, and capabilityto operate in harsh environments. They are also suitable for nuclear and aerospace applicationsdue to their low inertia and capability to be fed from a dc supply through a simple power converter.The principle of torque production in SRM makes rotor position information mandatory foreffective control of the drive. The torque produced by any particular phase of the SRM isdependent upon the exciting current and the period during which the current is carried by thatphase winding. The conduction period of any particular phase is termed as dwell angle whenit is specified in terms of rotor angular position. In the present work, the SRM operation has beenanalysed in sensor mode and in sensor-less mode, paying special attention to the relationshipbetween dwell angle and output torque ripple. The performance has been studied for differentvalues of dwell angle and the resultant torque profile has been analysed. From the analysis, amethodology has been devised to deduce an appropriate value of dwell angle for minimising thetorque pulsations, given the values of speed and load torque, thus improving the performanceof the SRM drive

Ultrasonic Bioreactor as a Platform for Studying Cellular Response

The need for tissue-engineered constructs as replacement tissue continues to grow as the average age of the world’s population increases. However, additional research is required before the efficient production of laboratory-created tissue can be realized. The multitude of parameters that affect cell growth and proliferation is particularly daunting considering that optimized conditions are likely to change as a function of growth. Thus, a generalized research platform is needed in order for quantitative studies to be conducted. In this article, an ultrasonic bioreactor is described for use in studying the response of cells to ultrasonic stimulation. The work is focused on chondrocytes with a long-term view of generating tissue-engineered articular cartilage. Aspects of ultrasound (US) that would negatively affect cells, including temperature and cavitation, are shown to be insignificant for the US protocols used and which cover a wide range of frequencies and pressure amplitudes. The bioreactor is shown to have a positive influence on several factors, including cell proliferation, viability, and gene expression of select chondrocytic markers. Most importantly, we show that a total of 138 unique proteins are differentially expressed on exposure to ultrasonic stimulation, using mass-spectroscopy coupled proteomic analyses. We anticipate that this work will serve as the basis for additional research which will elucidate many of the mechanisms associated with cell response to ultrasonic stimulation

Ultrasonic Bioreactor as a Platform for Studying Cellular Response

The need for tissue-engineered constructs as replacement tissue continues to grow as the average age of the world’s population increases. However, additional research is required before the efficient production of laboratory-created tissue can be realized. The multitude of parameters that affect cell growth and proliferation is particularly daunting considering that optimized conditions are likely to change as a function of growth. Thus, a generalized research platform is needed in order for quantitative studies to be conducted. In this article, an ultrasonic bioreactor is described for use in studying the response of cells to ultrasonic stimulation. The work is focused on chondrocytes with a long-term view of generating tissue-engineered articular cartilage. Aspects of ultrasound (US) that would negatively affect cells, including temperature and cavitation, are shown to be insignificant for the US protocols used and which cover a wide range of frequencies and pressure amplitudes. The bioreactor is shown to have a positive influence on several factors, including cell proliferation, viability, and gene expression of select chondrocytic markers. Most importantly, we show that a total of 138 unique proteins are differentially expressed on exposure to ultrasonic stimulation, using mass-spectroscopy coupled proteomic analyses. We anticipate that this work will serve as the basis for additional research which will elucidate many of the mechanisms associated with cell response to ultrasonic stimulation

Making sense of the bizarre behaviour of horizons in the McVittie spacetime

The bizarre behaviour of the apparent (black hole and cosmological) horizons of the McVittie spacetime is discussed using, as an analogy, the Schwarzschild-de Sitter-Kottler spacetime (which is a special case of McVittie anyway). For a dust-dominated "background" universe, a black hole cannot exist at early times because its (apparent) horizon would be larger than the cosmological(apparent) horizon. A phantom-dominated "background" universe causes this situation, and the horizon behaviour, to be time-reversed.Comment: 8 pages, 3 figure

Compositional Proteomics: Effects of Spatial Constraints on Protein Quantification Utilizing Isobaric Tags.

Mass spectrometry (MS) has become an accessible tool for whole proteome quantitation with the ability to characterize protein expression across thousands of proteins within a single experiment. A subset of MS quantification methods (e.g., SILAC and label-free) monitor the relative intensity of intact peptides, where thousands of measurements can be made from a single mass spectrum. An alternative approach, isobaric labeling, enables precise quantification of multiple samples simultaneously through unique and sample specific mass reporter ions. Consequently, in a single scan, the quantitative signal comes from a limited number of spectral features (≤11). The signal observed for these features is constrained by automatic gain control, forcing codependence of concurrent signals. The study of constrained outcomes primarily belongs to the field of compositional data analysis. We show experimentally that isobaric tag proteomics data are inherently compositional and highlight the implications for data analysis and interpretation. We present a new statistical model and accompanying software that improves estimation accuracy and the ability to detect changes in protein abundance. Finally, we demonstrate a unique compositional effect on proteins with infinite changes. We conclude that many infinite changes will appear small and that the magnitude of these estimates is highly dependent on experimental design

Association of Minimal Residual Disease With Superior Survival Outcomes in Patients With Multiple Myeloma: A Meta-analysis

Importance: Numerous studies have evaluated the prognostic value of minimal residual disease (MRD) in patients with multiple myeloma (MM). Most studies were small and varied in terms of patient population, treatment, and MRD assessment methods. Objective: To evaluate the utility of MRD detection in patients with newly diagnosed MM. Data Sources: A Medline search was conducted for articles published in English between January 1990 and January 2016. Study Selection: Eligible studies reported MRD status and progression-free survival (PFS) or overall survival (OS) in 20 or more patients following treatment. Among 405 articles identified, 21 met the initial eligibility criteria and were included in the analysis. Data Extraction and Synthesis: Information on patient characteristics, treatment, MRD assessment, and outcomes were extracted using a standard form. Main Outcomes and Measures: The impact of MRD status on PFS and OS was assessed by pooling data from relevant trials. Data were adjusted to allow for different proportions of patients with MRD in different studies, and analyzed using the Peto method. Forest plots were created based on Cox model analysis. Other prespecified research questions were addressed qualitatively. Results: Fourteen studies (n = 1273) provided data on the impact of MRD on PFS, and 12 studies (n = 1100) on OS. Results were reported specifically in patients who had achieved conventional complete response (CR) in 5 studies for PFS (n = 574) and 6 studies for OS (n = 616). An MRD-negative status was associated with significantly better PFS overall (hazard ratio [HR], 0.41; 95% CI, 0.36-0.48; P < .001) and in studies specifically looking at CR patients (HR, 0.44; 95% CI, 0.34-0.56; P < .001). Overall survival was also favorable in MRD-negative patients overall (HR, 0.57; 95% CI, 0.46-0.71; P < .001) and in CR patients (HR, 0.47; 95% CI, 0.33-0.67; P < .001). Tests of heterogeneity found no significant differences among the studies for PFS and OS. Conclusions and Relevance: Minimal residual disease-negative status after treatment for newly diagnosed MM is associated with long-term survival. These findings provide quantitative evidence to support the integration of MRD assessment as an end point in clinical trials of MM

Cosmological expansion and local physics

The interplay between cosmological expansion and local attraction in a gravitationally bound system is revisited in various regimes. First, weakly gravitating Newtonian systems are considered, followed by various exact solutions describing a relativistic central object embedded in a Friedmann universe. It is shown that the ``all or nothing'' behaviour recently discovered (i.e., weakly coupled systems are comoving while strongly coupled ones resist the cosmic expansion) is limited to the de Sitter background. New exact solutions are presented which describe black holes perfectly comoving with a generic Friedmann universe. The possibility of violating cosmic censorship for a black hole approaching the Big Rip is also discussed.Comment: 17 pages, LaTeX, to appear in Phys. Rev.

Black Holes in the Universe: Generalized Lemaitre-Tolman-Bondi Solutions

We present new exact solutions {which presumably describe} black holes in the background of a spatially flat, pressureless dark matter (DM)-, or dark matter plus dark energy (DM+DE)-, or quintom-dominated universe. These solutions generalize Lemaitre-Tolman-Bondi metrics. For a DM- or (DM+DE)-dominated universe, the area of the black hole apparent horizon (AH) decreases with the expansion of the universe while that of the cosmic AH increases. However, for a quintom-dominated universe, the black hole AH first shrinks and then expands, while the cosmic AH first expands and then shrinks. A (DM+DE)-dominated universe containing a black hole will evolve to the Schwarzschild-de Sitter solution with both AHs approaching constant size. In a quintom-dominated universe, the black hole and cosmic AHs will coincide at a certain time, after which the singularity becomes naked, violating Cosmic Censorship.Comment: 13 pages, 4 figure