Field Equations and Equations of Motion in Post-Newtonian Approximation of the Projective Unified Field Theory

The equations of motion of $N$ gravitationally bound bodies are derived from the field equations of Projective Unified Field Theory. The Newtonian and the post-Newtonian approximations of the field equations and of the equations of motion of this system of bodies are studied in detail. In analyzing some experimental data we performed some numeric estimates of the ratio of the inertial mass to the scalaric mass of matter.Comment: 17 page

Effects of diagram format and user numeracy on understanding cash flow data

An issue of longstanding concern in accounting information systems is the effective presentation and communication of financial data to users with little accounting background. Cash flow statements in particular have been singled out as difficult to interpret. To increase user understanding of cash flow data, this study explores the potential merits of diagram formats, as well as possible effects of the user’s numeracy skills. The study covers an experiment (N = 100) in which users were queried on their understanding of the cash flows of a real-world company, and in which type of format was either a cash flow statement or a cash flow diagram. Understanding was measured by three different concepts: interpretation accuracy, company diagnosis, and clarity of presentation. The study confirms that, on those measures, diagrams do not necessarily outperform cash flow statements, and that format familiarity (irrespective of the type of format) is a key driver in understanding cash flows. In addition, the study finds that numeric preference, but not numeric ability, helps in understanding cash flow data. The study discusses the sobering implications for designers of accounting information systems

Analysis of Nitrogen Loading Reductions for Wastewater Treatment Facilities and Non-Point Sources in the Great Bay Estuary Watershed

In 2009, the New Hampshire Department of Environmental Services (DES) published a proposal for numeric nutrient criteria for the Great Bay Estuary. The report found that total nitrogen concentrations in most of the estuary needed to be less than 0.3 mg N/L to prevent loss of eelgrass habitat and less than 0.45 mg N/L to prevent occurrences of low dissolved oxygen. Based on these criteria and an analysis of a compilation of data from at least seven different sources, DES concluded that 11 of the 18 subestuaries in the Great Bay Estuary were impaired for nitrogen. Under the Clean Water Act, if a water body is determined to be impaired, a study must be completed to determine the existing loads of the pollutant and the load reductions that would be needed to meet the water quality standard. Therefore, DES developed models to determine existing nitrogen loads and nitrogen loading thresholds for the subestuaries to comply with the numeric nutrient criteria. DES also evaluated the effects of different permitting scenarios for wastewater treatment facilities on nitrogen loads and the costs for wastewater treatment facility upgrades. This modeling exercise showed that: Nitrogen loads to the Great Bay, Little Bay, and the Upper Piscataqua River need to be reduced by 30 to 45 percent to attain the numeric nutrient criteria. Both wastewater treatment facilities and non-point sources will need to reduce nitrogen loads to attain the numeric nutrient criteria. The percent reduction targets for nitrogen loads only change minimally between wet and dry years. Wastewater treatment facility upgrades to remove nitrogen will be costly; however, the average cost per pound of nitrogen removed from the estuary due to wastewater facility upgrades is lower than for non-point source controls. The permitting options for some wastewater treatment facilities will be limited by requirements to not increase pollutant loads to impaired waterbodies. The numeric nutrient criteria and models used by DES are sufficiently accurate for calculating nitrogen loading thresholds for the Great Bay watershed. Additional monitoring and modeling is needed to better characterize conditions and nitrogen loading thresholds for the Lower Piscataqua River. This nitrogen loading analysis for Great Bay may provide a framework for setting nitrogen permit limits for wastewater treatment facilities and developing watershed implementation plans to reduce nitrogen loads

NGX-4010, a capsaicin 8% patch, for the treatment of painful HIV-associated distal sensory polyneuropathy: integrated analysis of two phase III, randomized, controlled trials

BACKGROUND HIV-associated distal sensory polyneuropathy (HIV-DSP) is the most frequently reported neurologic complication associated with HIV infection. NGX-4010 is a capsaicin 8% dermal patch with demonstrated efficacy in the treatment of HIV-DSP. Data from two phase III, double-blind studies were integrated to further analyze the efficacy and safety of NGX-4010 and explore the effect of demographic and baseline factors on NGX-4010 treatment in HIV-DSP. METHODS Data from two similarly designed studies in which patients with HIV-DSP received NGX-4010 or a low-concentration control patch (capsaicin 0.04% w/w) for 30 or 60 minutes were integrated. Efficacy assessments included the mean percent change from baseline in Numeric Pain Rating Scale (NPRS) scores to Weeks 2-12. Safety and tolerability assessments included adverse events (AEs) and pain during and after treatment. RESULTS Patients (n = 239) treated with NGX-4010 for 30 minutes demonstrated significantly (p = 0.0026) greater pain relief compared with controls (n = 100); the mean percent change in NPRS scores from baseline to Weeks 2-12 was -27.0% versus -15.7%, respectively. Patients who received a 60-minute application of NGX-4010 (n = 243) showed comparable pain reductions (-27.5%) to patients treated for 30 minutes, but this was not statistically superior to controls (n = 115). NGX-4010 was effective regardless of gender, baseline pain score, duration of HIV-DSP, or use of concomitant neuropathic pain medication, although NGX-4010 efficacy was greater in patients not receiving concomitant neuropathic pain medications. NGX-4010 was well tolerated; the most common AEs were application-site pain and erythema, and most AEs were mild to moderate. The transient increase in pain associated with NGX-4010 treatment decreased the day after treatment and returned to baseline by Day 2. CONCLUSIONS A single 30-minute application of NGX-4010 provides significant pain relief for at least 12 weeks in patients with HIV-DSP and is well tolerated. TRIAL REGISTRATION C107 = NCT00064623; C119 = NCT00321672

Bootstrap confidence sets for spectral projectors of sample covariance

Let $X_{1},\ldots,X_{n}$ be i.i.d. sample in $\mathbb{R}^{p}$ with zero mean and the covariance matrix $\mathbf{\Sigma}$. The problem of recovering the projector onto an eigenspace of $\mathbf{\Sigma}$ from these observations naturally arises in many applications. Recent technique from [Koltchinskii, Lounici, 2015] helps to study the asymptotic distribution of the distance in the Frobenius norm $\| \mathbf{P}_r - \widehat{\mathbf{P}}_r \|_{2}$ between the true projector $\mathbf{P}_r$ on the subspace of the $r$-th eigenvalue and its empirical counterpart $\widehat{\mathbf{P}}_r$ in terms of the effective rank of $\mathbf{\Sigma}$. This paper offers a bootstrap procedure for building sharp confidence sets for the true projector $\mathbf{P}_r$ from the given data. This procedure does not rely on the asymptotic distribution of $\| \mathbf{P}_r - \widehat{\mathbf{P}}_r \|_{2}$ and its moments. It could be applied for small or moderate sample size $n$ and large dimension $p$. The main result states the validity of the proposed procedure for finite samples with an explicit error bound for the error of bootstrap approximation. This bound involves some new sharp results on Gaussian comparison and Gaussian anti-concentration in high-dimensional spaces. Numeric results confirm a good performance of the method in realistic examples.Comment: 39 pages, 3 figure

An Algorithmic Theory of Integer Programming

We study the general integer programming problem where the number of variables $n$ is a variable part of the input. We consider two natural parameters of the constraint matrix $A$: its numeric measure $a$ and its sparsity measure $d$. We show that integer programming can be solved in time $g(a,d)\textrm{poly}(n,L)$, where $g$ is some computable function of the parameters $a$ and $d$, and $L$ is the binary encoding length of the input. In particular, integer programming is fixed-parameter tractable parameterized by $a$ and $d$, and is solvable in polynomial time for every fixed $a$ and $d$. Our results also extend to nonlinear separable convex objective functions. Moreover, for linear objectives, we derive a strongly-polynomial algorithm, that is, with running time $g(a,d)\textrm{poly}(n)$, independent of the rest of the input data. We obtain these results by developing an algorithmic framework based on the idea of iterative augmentation: starting from an initial feasible solution, we show how to quickly find augmenting steps which rapidly converge to an optimum. A central notion in this framework is the Graver basis of the matrix $A$, which constitutes a set of fundamental augmenting steps. The iterative augmentation idea is then enhanced via the use of other techniques such as new and improved bounds on the Graver basis, rapid solution of integer programs with bounded variables, proximity theorems and a new proximity-scaling algorithm, the notion of a reduced objective function, and others. As a consequence of our work, we advance the state of the art of solving block-structured integer programs. In particular, we develop near-linear time algorithms for $n$-fold, tree-fold, and $2$-stage stochastic integer programs. We also discuss some of the many applications of these classes.Comment: Revision 2: - strengthened dual treedepth lower bound - simplified proximity-scaling algorith