Rectifiable paths with polynomial log-signature are straight lines

The signature of a rectifiable path is a tensor series in the tensor algebra whose coefficients are definite iterated integrals of the path. The signature characterises the path up to a generalised form of reparametrisation. It is a classical result of K. T. Chen that the log-signature (the logarithm of the signature) is a Lie series. A Lie series is polynomial if it has finite degree. We show that the log-signature is polynomial if and only if the path is a straight line up to reparametrisation. Consequently, the log-signature of a rectifiable path either has degree one or infinite support. Though our result pertains to rectifiable paths, the proof uses results from rough path theory, in particular that the signature characterises a rough path up to reparametrisation.Comment: 11 page

The TGFβ type I receptor TGFβRI functions as an inhibitor of BMP signaling in cartilage.

The type I TGFβ receptor TGFβRI (encoded by Tgfbr1) was ablated in cartilage. The resulting Tgfbr1 Col2 mice exhibited lethal chondrodysplasia. Similar defects were not seen in mice lacking the type II TGFβ receptor or SMADs 2 and 3, the intracellular mediators of canonical TGFβ signaling. However, we detected elevated BMP activity in Tgfbr1 Col2 mice. As previous studies showed that TGFβRI can physically interact with ACVRL1, a type I BMP receptor, we generated cartilage-specific Acvrl1 (Acvrl1 Col2 ) and Acvrl1/Tgfbr1 (Acvrl1/Tgfbr1 Col2 ) knockouts. Loss of ACVRL1 alone had no effect, but Acvrl1/Tgfbr1 Col2 mice exhibited a striking reversal of the chondrodysplasia seen in Tgfbr1 Col2 mice. Loss of TGFβRI led to a redistribution of the type II receptor ACTRIIB into ACVRL1/ACTRIIB complexes, which have high affinity for BMP9. Although BMP9 is not produced in cartilage, we detected BMP9 in the growth plate, most likely derived from the circulation. These findings demonstrate that the major function of TGFβRI in cartilage is not to transduce TGFβ signaling, but rather to antagonize BMP signaling mediated by ACVRL1

Essays: Color-blind or Race-conscious Policies

The debate between advocates color blind and race conscious policies has been perennial in the United States since Reconstruction and has recently been resuscitated in the popular press with the publication of Michelle Alexander’s The New Jim Crow: Mass Incarceration in the Age of Color Blindness (2010). Alexander’s book provided support for the race conscious side and students read Nathan Glazer’s Affirmative Discrimination: Ethnic Inequality and Public Policy (1975) for a defense of the color blind side. The debate was framed in an even-handed manner by a selection from Desmond King and Rogers M. Smith’s Still a House Divided: Race and Politics in Obama’s America (2011) , which argues for both approaches under certain circumstances

Gratitude for Help among Adult Friends and Siblings

Peer reviewe

Entropy and Hausdorff Dimension in Random Growing Trees

We investigate the limiting behavior of random tree growth in preferential attachment models. The tree stems from a root, and we add vertices to the system one-by-one at random, according to a rule which depends on the degree distribution of the already existing tree. The so-called weight function, in terms of which the rule of attachment is formulated, is such that each vertex in the tree can have at most K children. We define the concept of a certain random measure mu on the leaves of the limiting tree, which captures a global property of the tree growth in a natural way. We prove that the Hausdorff and the packing dimension of this limiting measure is equal and constant with probability one. Moreover, the local dimension of mu equals the Hausdorff dimension at mu-almost every point. We give an explicit formula for the dimension, given the rule of attachment

2003 Philip C. Jessup International Law Moot Court Competition International Court Of Justice At The Peace Palace The Hague, Netherlands

The Republic of Annolay and the Republic of Reston have submitted the present dispute by Special Agreement to the International Court of Justice pursuant to Articles 36(1) and 40(1) of the Statute of the Court for final resolution

Using competency-based education to equip the primary health care workforce to manage chronic disease

The research reported in this paper is a project of the Australian Primary Health Care Research Institute, which is supported by a grant from the Australian Government Department of Health and Ageing under the Primary Health Care Research, Evaluation and Development Strategy

Prediction of lignin content in ruminant diets and faecal samples using rapid analytical techniques

The measurement of lignin content in ruminant diet and faecal samples is important for 2 digestibility studies, but it is typically time consuming and costly. The work reported 3 involved correlation of traditional wet chemistry data with that from three rapid instrumental 4 techniques, Fourier Transform Infrared spectroscopy (FTIR), Conventional 5 Thermogravimteric Analysis (TGA) and High Resolution TGA (MaxRes TGA) to predict 6 lignin content of diets and faeces from digestibility trials. Calibration and performance data 7 indicated that the FTIR model was acceptable for screening whilst the Conventional and 8 MaxRes TGA predictions were of high accuracy for quantitative analysis. Cross validation 9 and model performance data revealed that MaxRes TGA provided the best performing 10 predictive model. This work showed that MaxRes TGA can accurately predict lignin content 11 in ruminant diet and faecal samples with distinct advantages over traditional wet chemistry, 12 namely the requirement for small sample size, ease of sample preparation, speed of analysis 13 and high sample throughput at considerably lower cost

Association between dopaminergic polymorphisms and borderline personality traits among at-risk young adults and psychiatric inpatients

Background: In the development of borderline personality disorder (BPD) both genetic and environmental factors have important roles. The characteristic affective disturbance and impulsive aggression are linked to imbalances in the central serotonin system, and most of the genetic association studies focused on serotonergic candidate genes. However, the efficacy of dopamine D2 receptor (DRD2) blocking antipsychotic drugs in BPD treatment also suggests involvement of the dopamine system in the neurobiology of BPD.Methods: In the present study we tested the dopamine dysfunction hypothesis of impulsive self- and other-damaging behaviors: borderline and antisocial traits were assessed by Structured Clinical Interview for Diagnosis (SCID) for DSM-IV in a community-based US sample of 99 young adults from low-to-moderate income families. For the BPD trait analyses a second, independent group was used consisting of 136 Hungarian patients with bipolar or major depressive disorder filling out self-report SCID-II Screen questionnaire. In the genetic association analyses the previously indicated polymorphisms of the catechol-O-methyl-transferase (COMT Val158Met) and dopamine transporter (DAT1 40 bp VNTR) were studied. In addition, candidate polymorphisms of the DRD2 and DRD4 dopamine receptor genes were selected from the impulsive behavior literature.Results: The DRD2 TaqI B1-allele and A1-allele were associated with borderline traits in the young adult sample (p = 0.001, and p = 0.005, respectively). Also, the DRD4 -616 CC genotype appeared as a risk factor (p = 0.02). With severity of abuse accounted for in the model, genetic effects of the DRD2 and DRD4 polymorphisms were still significant (DRD2 TaqIB: p = 0.001, DRD2 TaqIA: p = 0.008, DRD4 -616 C/G: p = 0.002). Only the DRD4 promoter finding was replicated in the independent sample of psychiatric inpatients (p = 0.007). No association was found with the COMT and DAT1 polymorphisms.Conclusions: Our results of the two independent samples suggest a possible involvement of the DRD4 -616 C/G promoter variant in the development of BPD traits. In addition, an association of the DRD2 genetic polymorphisms with impulsive self-damaging behaviors was also demonstrated. © 2010 Nemoda et al; licensee BioMed Central Ltd