Abstract:
Theorem 1 Let F:N-->R stand for any function which a) $F$ monotonically weakly increases; b) $F$ tends to infinity; and c) such that $q/F(q)$ tends to infinity. Let Z_F(q) equal the number of divisors of q less than sqrt{F(q)} minus the number of divisors of q between sqrt{F(q)} and F(q). Then, on the average, Z_F(q) equals Euler's constant Theorem 2 Fix a in (0,1). Write A for the average number of divisors of n that lie in (0,sqrt{a n}) minus the number of that lie in (sqrt{a n},a n)$. Then A= (sum_{i=1}^{\lceil {1-a}/a \rceil} \frac{1}{i}) - ln(1/a).

Abstract:
We use a probabilistic interpretation of solid angles to generalize the well-known fact that the inner angles of a triangle sum to 180 degrees. For the 3-dimensional case, we show that the sum of the solid inner vertex angles of a tetrahedron T, divided by 2*pi, gives the probability that an orthogonal projection of T onto a random 2-plane is a triangle. More generally, it is shown that the sum of the (solid) inner vertex angles of an n-simplex S, normalized by the area of the unit (n-1)-hemisphere, gives the probability that an orthogonal projection of S onto a random hyperplane is an (n-1)-simplex. Applications to more general polytopes are treated briefly, as is the related Perles-Shephard proof of the classical Gram-Euler relations.

Adaptation is the pursuit of active,deliberate measures to enhance humankind’s capacity to manage water supply and attenuate demand in the face of climate uncertainty. This article contends that worsening constraints upon freshwater due to climate variability demand concerted, imaginative, science-based solutions. These solutions must join creative management to co-production of climate knowledge. Through a series of case studies, we analyze the need for adaptation approaches to prevail over climate variability, and the role of these factors to facilitate their implementation. We also examine how translation of climate knowledge is helping spur adaptation at various spatial levels. These experiences point to the challenges in adaptation, andthe adversity various regions will be faced if we do not.

Abstract:
We investigate a new class of entangled states, which we call 'hyperentangled',that have EPR correlations identical to those in the vacuum state of a relativistic quantum field. We show that whenever hyperentangled states exist in any quantum theory, they are dense in its state space. We also give prescriptions for constructing hyperentangled states that involve an arbitrarily large collection of systems.

Abstract:
Pyruvate dehydrogenase kinase 4 (PDK4) inhibition by nuclear factor-κB (NF-κB) is related to a shift towards increased glycolysis during cardiac pathological processes such as cardiac hypertrophy and heart failure. The transcription factors estrogen-related receptor-α (ERRα) and peroxisome proliferator-activated receptor (PPAR) regulate PDK4 expression through the potent transcriptional coactivator PPARγ coactivator-1α (PGC-1α). NF-κB activation in AC16 cardiac cells inhibit ERRα and PPARβ/δ transcriptional activity, resulting in reduced PGC-1α and PDK4 expression, and an enhanced glucose oxidation rate. However, addition of the NF-κB inhibitor parthenolide to these cells prevents the downregulation of PDK4 expression but not ERRα and PPARβ/δ DNA binding activity, thus suggesting that additional transcription factors are regulating PDK4. Interestingly, a recent study has demonstrated that the transcription factor E2F1, which is crucial for cell cycle control, may regulate PDK4 expression. Given that NF-κB may antagonize the transcriptional activity of E2F1 in cardiac myocytes, we sought to study whether inflammatory processes driven by NF-κB can downregulate PDK4 expression in human cardiac AC16 cells through E2F1 inhibition. Protein coimmunoprecipitation indicated that PDK4 downregulation entailed enhanced physical interaction between the p65 subunit of NF-κB and E2F1. Chromatin immunoprecipitation analyses demonstrated that p65 translocation into the nucleus prevented the recruitment of E2F1 to the PDK4 promoter and its subsequent E2F1-dependent gene transcription. Interestingly, the NF-κB inhibitor parthenolide prevented the inhibition of E2F1, while E2F1 overexpression reduced interleukin expression in stimulated cardiac cells. Based on these findings, we propose that NF-κB acts as a molecular switch that regulates E2F1-dependent PDK4 gene transcription.

Abstract:
We establish new relations which connect Euclidean sonar transforms (integrals taken over spheres with centers in a hyperplane) with classical Radon transforms. The relations, stated as operator identities, allow us to reduce the inversion of sonar transforms to classical Radon inversion.

Abstract:
In this work we analyze the sample complexity of classification by differentially private algorithms. Differential privacy is a strong and well-studied notion of privacy introduced by Dwork et al. (2006) that ensures that the output of an algorithm leaks little information about the data point provided by any of the participating individuals. Sample complexity of private PAC and agnostic learning was studied in a number of prior works starting with (Kasiviswanathan et al., 2008) but a number of basic questions still remain open, most notably whether learning with privacy requires more samples than learning without privacy. We show that the sample complexity of learning with (pure) differential privacy can be arbitrarily higher than the sample complexity of learning without the privacy constraint or the sample complexity of learning with approximate differential privacy. Our second contribution and the main tool is an equivalence between the sample complexity of (pure) differentially private learning of a concept class $C$ (or $SCDP(C)$) and the randomized one-way communication complexity of the evaluation problem for concepts from $C$. Using this equivalence we prove the following bounds: 1. $SCDP(C) = \Omega(LDim(C))$, where $LDim(C)$ is the Littlestone's (1987) dimension characterizing the number of mistakes in the online-mistake-bound learning model. Known bounds on $LDim(C)$ then imply that $SCDP(C)$ can be much higher than the VC-dimension of $C$. 2. For any $t$, there exists a class $C$ such that $LDim(C)=2$ but $SCDP(C) \geq t$. 3. For any $t$, there exists a class $C$ such that the sample complexity of (pure) $\alpha$-differentially private PAC learning is $\Omega(t/\alpha)$ but the sample complexity of the relaxed $(\alpha,\beta)$-differentially private PAC learning is $O(\log(1/\beta)/\alpha)$. This resolves an open problem of Beimel et al. (2013b).

Abstract:
We present ROS- and diabetes-related targets (genes/proteins) collected from the biomedical literature through a text mining technology. A web-based literature mining tool, SciMiner, was applied to 1,154 biomedical papers indexed with diabetes and ROS by PubMed to identify relevant targets. Over-represented targets in the ROS-diabetes literature were obtained through comparisons against randomly selected literature. The expression levels of nine genes, selected from the top ranked ROS-diabetes set, were measured in the dorsal root ganglia (DRG) of diabetic and non-diabetic DBA/2J mice in order to evaluate the biological relevance of literature-derived targets in the pathogenesis of diabetic neuropathy.SciMiner identified 1,026 ROS- and diabetes-related targets from the 1,154 biomedical papers (http://jdrf.neurology.med.umich.edu/ROSDiabetes/ webcite). Fifty-three targets were significantly over-represented in the ROS-diabetes literature compared to randomly selected literature. These over-represented targets included well-known members of the oxidative stress response including catalase, the NADPH oxidase family, and the superoxide dismutase family of proteins. Eight of the nine selected genes exhibited significant differential expression between diabetic and non-diabetic mice. For six genes, the direction of expression change in diabetes paralleled enhanced oxidative stress in the DRG.Literature mining compiled ROS-diabetes related targets from the biomedical literature and led us to evaluate the biological relevance of selected targets in the pathogenesis of diabetic neuropathy.Diabetes is a metabolic disease in which the body does not produce or properly respond to insulin, a hormone required to convert carbohydrates into energy for daily life. According to the American Diabetes Association, 23.6 million children and adults, approximately 7.8% of the population in the United States, have diabetes [1]. The cost of diabetes in 2007 was estimated to be $174 billion

Abstract:
We demonstrate here that thiol-ene chemistry can be used to provide side-chain functionalized monomers based on 3,4-propylenedioxythiophene (ProDOT) containing ionic, neutral, hydrophobic, and hydrophilic side chains. All reactions gave high yields and purification could generally be accomplished through precipitation. These monomers were polymerized either chemically or electro-chemically to give soluble materials or conductive films, respectively. This strategy provides for facile tuning of the solubility, film surface chemistry, and film morphology of this class of conducting polymers.

Abstract:
We present exact results for two complementary measures of spatial structure generated by 1D spin systems with finite-range interactions. The first, excess entropy, measures the apparent spatial memory stored in configurations. The second, statistical complexity, measures the amount of memory needed to optimally predict the chain of spin values. These statistics capture distinct properties and are different from existing thermodynamic quantities.